If y(x) satisfies the differential equation y" + x²y = 0, where y(0) = yo and y'(0) = y, show that its transform Y(p) satisfies the equation Y" +p?Y = pyo + yo- %3D

Q: What are the P(x) and Q(x) of y' =y-xy³e2Xrespectively?

A: Given the differential equation is: Since

Q: Form the partial differential equation by eliminating the arbitary from z=xy+f(x2+y2)

A: Form the partial differential equation by eliminating the arbitary from z=xy+f(x2+y2)

Q: Prove that the differential equation is not exact ey (e" + ") - s/ = 0 2+ + -

A: Exact diffretaial equation

Q: (c) 2ry'y-y²+²=0.

A: 2xy'y-y2+x2=0⇒2xyy'=y2-x2

Q: Show that the transformation 2 = ln x transforms the differential equation 2 x ²³y" + Axy' + By=0…

A:

Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

A:

Q: - Transform y' =- to a possible standard form of first ordered linear differential equation. *+G-1)…

A:

Q: 8²% Classify the partial differential equation: 6- dx² -16 <0, Hyperbolic -24 < 0, Elliptic O 240,…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: (x - v)y" - v =tanx is second order Ilinear differential equation. Select one: O True O False

A:

Q: y2(1+(y')2)=x+y'y find the general solution to the equation.

A:

Q: Obtain the differential equation of a parabola with axis parallel to the x-axis. A 3(y")²-y'y"=0 B…

A:

Q: y ce + 3r O y'+6y 2t (t+ 1) O y'+2y = / (1+ 6) 3. y'-2y 61 (t- 1) O y'+ 2y = 61 (1 + 1)

A:

Q: Transform the differential equation 2y′′−y′+4y=e^(mt) y(0) = 2  y'(0)= 5 a )into an algebraic…

A:

Q: Consider the differential equations y' = x + y²,y' = x - y²₁ y² = -x - y². The slope field depicted…

A: Given differential equationsslope field are calculated by analyzing equilibrium points or nullclines

Q: Find the solution for this second ODE y(0) = 1, y'(0) = 1

A:

Q: Determine the solution of the differential equation shown using Laplace and Inverse Laplace…

A: Given y'''−y=4e−x+3e2x.....1 When, x=0, y=0, y'=−1 and y''=2 Take Laplace transformation of equation…

Q: y (2 xy +1)= xy'

A:

Q: Form the differential equation for the function 2xy= asin2x -bcos2x O a. xy" +2y' = – 4xy O b. xy"…

A:

Q: Cx²e*dx

A:

Q: Find the general solution of the DE (x + y)dx + (x - y)dy =0.

A: Given differential equation is(x+y)dx+(x-y)dy=0Here, M=x+y and N=x-ythen ∂M∂y=1 and…

Q: The slope field for the equation y' = -x -y is shown below On a print out of this slope field,…

A: The slope field for the equation y'=-x-y passes through 1,0

Q: -80- 60- 40 20 20 40 60 80 100 120

A: First you have to note that this piecewise function graph indicate that a lot of different functions…

Q: Find the ordinary differential equation of a circle which passes through the points (0,0) and (2,0).

A: We will find out the required differential equation for given circle.

Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

A:

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.