Q3- Solve nonexact D. E x dx+(3y4+y+3x2y2) dy 0.

Q: Solve: D₁(r(t) = u(t)) X r(t) = 6ti - 4t³j + 5t²k u(t) = -2i+ 5t²j - 6t³k

A: The given vectors are  r(t)=6ti-4t3j+5t2ku(t)=-2i+5t2j-6t3k The objective is to calculate the value…

Q: d²y Solve the particular solution for = 2 – 4x when points (0, 2) and (-1, 3) are on the dx2 curve.

A:

Q: Find the general solution of dy -2x6 dx y-4

A:

Q: Solve the D.E. 3(3x? + y²) dx - 2xy dy = 0 (A x= c(x² + 9y²) B x= c(x2 + 3y3) © x = c(9x² + y²) D x…

A:

Q: dy = y + Vx² + y² dr Find the general solution of x-

A:

Q: Q4/ solve the following equations. d²y dy + 81 = 0 dx2 dx

A:

Q: (x+xy²)dxte*, ydy=D0

A: Given: x+xy2dx+ex2ydy=0 ⇒x1+y2dx+ex2ydy=0 ⇒ex2ydy=-x1+y2dx ⇒y1+y2dy=-xex2dx

Q: Solve the D.E 9+4y = Sec2X %3D

A:

Q: Solve the non-homo. D.E. 1.y" + y = 3e2x

A:

Q: A. Find the general solution of y" = 12x². dy B. Solve for y F dx - 4 x²-1

A: The given differential equations A) y''=12x2 B) dydx=4x2-1 use the integration formulas,…

Q: A Solve 2-3x dy x.y dx B Solve (D2 +D-2)y e*

A:

Q: Solve: (4x3y−18x2−y)dx + (x4+3y2−x)dy = 0 a) Check for exactness b) If the equation is exact,…

A: Exact differential equation

Q: dy = -8xy² dx 3. Solve + 4x(4x+1) y-(8.x² +4x² -1) by knowing u =x is a solution.

A: Given: dydx=-8xy2+4x4x+1y-8x3+4x2-1

Q: Solve this DE (D2+2D+2)y = e-xcscx

A:

Q: [1] Solve for the GS of (D4-5D³+9D²-7D+2)y=0

A: By Bartleby policy I have to solve only first one as these are unrelated problems.These are…

Q: The solution of (D² – 4D+13)y 0 5 2x (A eix . Be Jox (A ex + Be)

A: D2-4D+13y=0 The auxiliary equation is m2-4m+13=0 ⇒m=4±-42-4132⇒m=2±3i

Q: d?y dy Solve by D operator method dx2 20+y = x²e 3x.

A: Given differential equation is d2ydx2 - 2dydx + y = x2e3x

Q: Q: Solve : -4t y +2y - Jydt =e s(t-3) | yco) = 0 ,y'co) = 0 %3D

A: The given differential equation is: y''+2y'-∫0t y dt=e-4t δ(t-3) ;        y(0)=0,  y'(0)=0…

Q: Find the solution. dy + 5y =2x?y4 dx X- 6 x²+cx15 13 A 6. -2– cx 15 B 23 © cy-1 = 6. ?+x15 13 D 6 y…

A:

Q: Solve (D5 – 2D4 + 4D³ – 8D²) y = 48e-2 16 sin (2x) - = A- B I = E E E P & O

A:

Q: Find the particular solution of -4y = 3x – 1 given that when x=0, y=0 and d2x dx dx II

A:

Q: Solve for the solution of this D.E. y''' + 2y'' - 5y'-6y=0 Which has values of y=3, y'=6. y''=12…

A: Now , we have a homogenous differential equation . y'''+2y''-5y'-6y=0y(0)=3y'(0)=6y''(0)=12 We find…

Q: Q9. Solve (x3 + уз)dy + x2y dх %3D0

A:

Q: B) Solve (3x? + 3x y²)dx + (3x²y – 3y² + 2y)dy = 0 %3D

A: First test for exactness:  ∂∂y3x2+3xy2=6xy ∂∂x3x2y-3y2+2y=6xy Since, ∂∂x3x2y-3y2+2y=∂∂y3x2+3xy2 so…

Q: Q2: solve the equation dx 2x dy y y 3.

A:

Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: A Q2 Show that y=x+ is the solution of 3x – x = x+ y. dy dx

A:

Q: SOlve the differentilal equation d²y d*y 4- d³y + 7. dx2 14 | dx+ dx3

A:

Q: Solve and find the domain in which the solution is defined. dy/dx = (y2-xy-x2)/x2 , y(-3)=-6

A:

Q: Solve the following d'y 8- + 16y = 9e2 dx? d'y dx4 using the method of undetermined coefficients.

A: The solution is given as

Q: Solve the equation: 8d3y/dx3 -5dy/dx+3y x3, for x, with initial values of (d3y/dx3 (0) = 4) and y…

A:

Q: solve the D. y +8y" +16Y

A: We have to solve the differential equation.                                  y''''+8y''+16y=0 can…

Q: d²y dy Solve 4 +4y = 3e2x. - dx2

A:

Q: Check that y Cx) = e* is the Solution of y" + y' - 2y = 0

A:

Q: Solve for the solution of: (D3 + D)2y = 0

A:

Q: (a) Solve (2ry + y²) dy = –(x² + y²) dx y(1) = 2

A:

Q: Find the solution. d3x d?x d³x dx + 2 =0 dr3 dr? dt

A:

Q: Solve the equation by using the method of variation of parameters dy 2dy 22 + 2y = e“ csc x. dx dx2

A: Let us consider the second order differential equation y''+py'+qy=g(t) Determine the complementary…

Q: Solve the equation: ydx + 3x – xy + 2)dy = 0

A: Given: ydx+3x-xy+2dy=0

Q: Q4/ solve the following equations. d²y dy + 81- = 0 dx² dx

A:

Q: Solve the D.E. 3(3x +y) dx - 2xy dy = 0 A x- c(9x² +y°) B) x- c(x² + 9y³) © x- c(9x² +y°) D x- c(x²…

A: Given Equation: 3(3x2+y2)dx-2xydy=0 ⇒3(3x2+y2)dx=2xydy ⇒dydx=3(3x2+y2)2xy------(i)

Q: Solve : -4t y +2y -J ydt = e s(t-3) yco) = 0 ,y'co)= o y'co) =

A: Convert the given equation in Laplace domain: s2Y+2sY-Ys=e-34+ss3+2s2-1Y=se-34+sY=se-34+ss3+2s2-1

Q: Solve the follawing D ·E. 2. y²dx + (3xy +y²-1) dy =0

A: Please refer the attached image for complete solution.

Q: Find the solution. dy x-+5y=2x3y4 dx A y = -x+Cx13 15 6. -2-cx 15 23 B y = CX x²+cx 15 y = -

A: Given differential equation is xdydx + 5y = 2x2y4

Q: nd Solve:- Qz: Chassify - 3x dy +(3X+リ』= e

A:

Q: Q1:- Solve the following DEs:- dy + 2x³y = y³x3 dx

A:

Q: Solve (D2+4D+4)y=e-x sin 2x

A:

Q: Solve the equation xd2y/dx2-dy/dx+4x^3y=x^5

A: Consider the provided D.E,

Q: Solve dʻy - 2x- xe 2x– xe dx² by using the undetermined coefficient method.

A:

Q: Q/ Solve the DEs: 1-a+yxdx+(1+x)dy = 0

A: 1-(1+y2)dx+(1+x2)dy=0

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.