Find an integrating factor for the differential equation 3y + 2t ) dt + 3 dy = 0 t2 t2 (justify your answer) and then the general solution to the ODE.

Q: Find the general solution to the differential equation. dx = 3t2(x2 + 16) dt %3D 4 tan(4°) + C x =

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Q: +2y = t² – t + 1, y(1) = dt

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Q: dP VPt. P(1) = 2 dt %3D

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Q: Find the solution of the differential equation that satisfies the given initial condition. dL = kL²…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

A: Given: f'(x)=6x f(0)=8 Integrate the equation. ∫f'(x)=∫6xf(x)=6x22+Cf(x)=3x2+C

Q: (A) Find the integration factor of the non exact differential equation ev (x² + +1]dx + ( +2y dy=0…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

A: Explanation: Given that,  f''(x)=sinxf'(0)=1f(0)=6       Concept Used:

Q: Find the solution of the differential equation that satisfies the given initial condition dP = 4√…

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Q: Find the solution of the differential equation that satisfies the given initial condition. du - 2t +…

A: The given differential equation is, dudt=2t+sec2t2u Apply Separation of Variables method,…

Q: Find the particular solution of the differential equation that satisfies the initial condition. dy…

A: Given differential dydx=116-x2 dy=116-x2dx Integrating both sides ∫dy=∫116-x2dx We know that…

Q: Solve the final solution for the differential equation with initial values: y(0) = 2 & y'(0) = 6.…

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Q: Evaluate the differential equations: Integrating Factor by Formula a) (2y2 + 2y + 4x2)dx + (2xy +…

A: Given:  a) 2y2+2y+4x2dx+2xy+xdy=0b) y2cosxdx+4+5ysinxdy=0

Q: Find the explicit general solution to the differential equation. Hint: Homogeneous. xy + y? – x²y' =…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dy %3D…

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Q: Solve the final solution for the differential equation with initial values: y(0) = 2 & y'(0) =6. Use…

A: The given initial value problem is                                             y''-3y'+2y=6 ;…

Q: Find the solution of the differential equation dy dy + 4: + 4y = 20t, dt dt? satisfying the initial…

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Q: Solve the differential equation. dz + 4et + z = 0 dt %3D - In(#|) z = C+

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Q: Solve the differential equation that satisfies the given initial condition: dy xe",where y(2) = 0 dx…

A: We first separate the variables and then integrate  C= integrating constant

Q: . Find the integrating factor of the first ordered linear differential equation, (x + 3y)dx – xdy =…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dL kL2…

A: the given differential equation is , dLdt=kL2ln(t) , L(1)=-5

Q: Find the solution of the differential equation that satisfies the given initial condition. dP 4V Pt,…

A: The given differential equation is dPdt=4Pt, P1=5. Used formulae: xn=nxn-1. ∫xndx=xn+1n+1+C

Q: Find the solution of the differential equation that satisfies the given initial condition. dp dt 7√…

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Q: (A) Find the integration factor of the non exact differential equation 2y +1 e +2y

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Q: Find the solution of the differential equation that satisfies the given initial condition. du 2t +…

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Q: 2. For the differential equation d`y dy -8y 8e, find the solution 4. 4 - dt dt a) Using the Method…

A: 2. Given differential equation is 4d2ydt2-4dydt-8y=8e-t A) Using method of variation of parameters…

Q: The integrating factor that transforms the differential equation 3y" – 6y' + Axy = 0 , into a…

A: The differential equation of the form, A(x)d2ydx2+B(x)dydx+C(x)y=0 can be transformed into a…

Q: Determine the general solution to the differential equation dy +4x° = yx dx Use a "c" to denote the…

A: We have to find the general solution of the differential equation dydx+4x5=yx5.

Q: By using the substitution z = y², convert the differential equation dy x²y- xy2 = 1. dx to a linear…

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Q: (a) Use the integrating factor method to solve the differential equations dy + (1+ x)y = e¯*; y(1) =…

A: It is a linear differential equation of order 1 and gence we will first find its integrating factor…

Q: y" - 3y' + 2y = 6

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Q: in the form of differential equation shown below; where the initial conditions are z d²y dy + 10 dt…

A: In the given question, concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: (a) Use the integrating factor method to solve the differential equations dy (1+x)y = e*; y(1) = 0…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dP dt =…

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Q: Find the general solution of the given differential equations by the concept of Exact DE and…

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Q: Show that the substitution v=ax+by+c transforms the differential equation dy/dx=F(ax+by+c)into a…

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Q: (e²y + te³y)dt + (te²+2) dy=o Initial condition: y(o)=-1

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Q: dy x sin x y(0) = –1 6. dx y

A: Given : dydx=xsinxy. By simplifying, we get: ydy=xsinx Take integration on both sides, we get:…

Q: Find the particular solution of the differential equation that satisfies the initial condition. 1 dy…

A: Given: dydx=116-x2 ;  y(0)=π

Q: w (1) = 1 -+ xtu (t) dt, u (0) = 0

A: The given integro-differential  equation is                u'(x)=1-13x +∫01xtu(t)dt with initial…

Q: Find a general solution of the given differential equation. d²y dy 2-+ y = e'tan-1t dt2 dt

A: Given differential equation is  d2ydt2-2dydt+y=ettan-1t Associated homogeneous differential equation…

Q: Find the solution of the differential equation that satisfies the given initial condition. dP dt 2…

A: It is given that,dPdt=2Pt , P1=5Find the solution of the differential equation that satisfies the…

Q: Convert the equation d°y dy -3 x y 0 dx3 -3. and initial conditions y(0)= 1.11983, y'(0)=0.83697 and…

A: Introduction: A higher order linear differential equation can be converted into a system of first…

Q: Find the solution of the differential equation that satisfies the given initial condition. dP dt =…

A: Given that: dPdt=8Pt         and P(1)=6

Q: Find the fundamental set of solutions for the differential equation d²y + a²y = 0, a#0. dt2

A: We need to find Fundamental set of solutions for the given differential equation. d2ydt2+a2y=0…

Q: Find the solution of the differential equation that satisfies the given initial condition. dP = 4 dt…

A: Given: dPdt=4Pt, P(1)=5 We will solve the given differential equation by the variable separable…

Q: Find the solution of the differential equation that satisfies the given initial condition. 2t +…

A: The given differential equation is dudt=2t+sec2(t)2u⇒2u du=2t+sec2(t) dt ..................... (1)

Q: Find the particular solution of the differential equation that satisfies the initial condition(s). f…

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Q: Solve this system of simultaneous differential equations. 3 at + = 2e dt dy + 8 y dy + 4 x + dt = t…

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Q: Find the solution of the differential equation that satisfies the given initial condition. dy xey,…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.