Exercise 7 Find the general solution 1. 6y'dx - x(2x + y)dy = 0

Q: 5. Show that the differential equation y" +a²y = f(x), y(0) = y'(0) = 0, has 1 y(x) = -…

A: proof:-we have          y(x)=1a∫0xf(t)sina(x-t)dt   ⋯(i) differentiate by leibnitz's rule(i) , we…

Q: dr The differential equation dt2 -)² + sin() +1= 0 has degree dt dt (a) 3 (b) 2 (c) 1 (d) not…

A: We’ll answer the first question. Please submit a new question specifying the one you’d like…

Q: integrate t2 sin(2t) dt from 0 to 8pi

A: We will  Integrate by parts using the formula:              ∫u v dx = u∫v dx −∫u' (∫v dx) dx.

Q: (1) Find the general solution for -) dx - -) dy = %3D

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Q: Solve the differential equation using Laplace transform of y"+y=6sin2t ; when y(0)=3 and y'(0)=1

A: The given differential equation is…

Q: A solution to the partial differential equation. 9. is dy?

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Q: Use integration to find a general solution of the differential equation        dy/dx = 4x2 + 7

A: Given ,     dydx=4x2+7      dy=4x2+7dxThis is variable seperable form .

Q: Exercise 2.7 dy 2cosx-sin². -sin x+ y 1. Verify that y, = sinx is a solution to and solve the %3D…

A: Note:- As per our guidelines, We can answer the first question since the exact one wasn’t specified.…

Q: Make the Non exact differential equation xy dx+(3y^2+2x^2−20) dy=0 to an exact differential…

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Q: The differential equation y²x + 2y'eª = 0 is Select one: Linear Exact Seperable Homogeneous

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Q: Form the partial differential equation by eliminating the arbitrary function z =x+y+f(xy)

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Q: Find the solution to the differential equation dz/dt=7te^(5z) that passes through the origin.

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Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: The roots of an auxiliary cubic equation are m1=-1 and m2=m3=-5. What is the corresponding…

A: We have given the roots of an auxiliary cubic equation ,  m1 = -1  , m2 = m3 = -5 Thus , Auxiliary…

Q: What is an integrating factor of the nonexact DE  (2y^2 + 3x) dx + xydy = 0 ?

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Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A: Cross multiply first to take x terms on a side and y terms on another side. Then integrate both…

Q: Solve the solutions of (e + Iny +) dz + ( + + In r + siny) dy %3D

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Determine the equation of the curve passing through the origin in the from y = f(x) which satisfies…

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Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: form the partial differential equation by eliminating the arbitrary function from z=xy+f(x2+y2)

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Q: Calculate the solution to the differential equation -ry 0 with bound- dr dy %3D ary values y = 1 and…

A: We have to find the solution

Q: Determine the integrating factor xydy - (y2-3x2)dx = 0

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Q: If y = eex the y' - y" + exy' is equal to?

A: The given equation is y=eex

Q: Compute the differential dy  for  y=(6x+sinx)^3

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Q: tan(3x + 8). Let y : Find the differential dy when x = 5 and dx = 0.4 Find the differential dy when…

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Q: Find the solution of the partial differential equation- = 3 dt? by variable separable method

A: given partial differential equation  ∂2z∂x2=3∂2z∂t2 to find -solution of the partial differential…

Q: Use a computer algebra system to graph the slope field for the differential equation and graph the…

A: The differential equation is dydx=0.8y, y(0)=4. Solve the equation as follows.…

Q: Derive a differential equation for the orthogonal trajectories of the family  of curves xy=c

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Q: Show that y is a solution of differential equation = 1-. dy %3D dx

A: y'(x)=1-yx We can simplify it as: dydx+yx=1First-order linear ordinary differential equation.…

Q: Find the differential equation of the family of parabolas with vertex ar Focus on the x-axis * O y =…

A: We have to find

Q: The Integrating factor of the equation (x²y³ + xy) dy dx 1 is

A: We have to find the integration factor of the equation x2y3+xydydx=1. We know that integrating…

Q: Is the differential equation (uv+u)du = [(u^2)*(v^2) + u^2 + v^2 + 1]dv separable?

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Q: Find the general solution of the differential equation and check the result by differentiation.…

A: On simplification, we get Now integrating on both sides, we get

Q: Find the solution of non linear partial differential du equation ди = U бу dx

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Q: Form the partial differential equation by eliminating arbitrary function from z = e" f(x – y)

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Q: The formation of the partial differential equation by eliminating arbitrary function of z = 5f(x" –…

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Q: Solve the system of ordinary differential equations defined by dx/dt+y = cost dy/dt+x = −sint

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Q: dy Obtain general solution of- 3/xy dx

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Q: Use Euler method to estimate the solution of 1 sin 5x - 5e cos 5.x, dx with initial condition v(0)=0…

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Q: Classify the partial differential equation +34 = sin(3x + 4y).

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Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

Q: Find the solution. 7. (3siny – 5x)dx + 2x2cotydy = 0 hint: let z = siny

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Q: Find the solution to the differential equation  dz/dt=7tez that passes through the origin. z=?

A: We have to find the solutions

Q: Use integration to find a general solution of the differential equation                dy/dx = sin…

A: given differential equation as dydx= sin 2x or it can be written as dy=sin 2x dx

Q: dy - 1 = siny dx

A: Given : dydx-1=siny To Find : solution of Given DE

Q: The partial differential equation is classified as a. hyperbolic O b. parabolic O. Circular o d.…

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Q: Obtain the particular solution. 1. 2y dx = 3x dy ; when x = 2 , y = -1 .

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