: Discuss the existence and unique solution for the IVP y'= 3y3, y (0)=0

Q: 5. Find a second solution to (1 – a2) y" + 2xy' = 0, given one solution y1(x) = 1.

A:

Q: 7. Find the general solution to y″ – 2y' = 2e²t.

A: To solve the differential equation y′′−2y′=2e2t, we first find the associated homogeneous equation…

Q: Find the general solution of (1+ x²)y' + xy = x=1(1 +x²)-/½

A:

Q: Solve the DE x²y"+xy'+ (x²-÷) y=x³/2, given that Yı=x-1/2sinx and y2=x-1/2cosx are two solutions of…

A: Given the given DE is x2y"+xy'+x2-14y=x32. y1=x-12sinxy2=x-12cosx

Q: Зу² — 4x + (6xy +^)y' = 0.

A:

Q: Find a particular solution to 11.5e5t y" – 10y + 25y t2 +1 Yp %3D

A:

Q: Find the volume of the solid bounded by the cylinders x² + z² = 1 and y² + z² = 1.

A: The given problem is to find the volume of the solid bounded by the given cylinders x2+z2=1 and…

Q: 4. Find the complete solution of 2x³y' = y(y² + 3x²) %3D

A:

Q: x²y" − x(x + 2)y' + (x + 2)y = 0, 0

A: According to the given data, find the general solution:

Q: 3. Find the general solution of the following DE. y' = 3 (y + 1) O y = ce³x - 1 3y = ce³x - 1 Oy =…

A: Use variable separable to Solve this problem.

Q: dy dt 13.1 y – 13.94 y²; y(0) = 0.03

A: Given,dydt=13.1y-13.94y2113.1y-13.94y2dy=dt1y13.1-13.94ydy=dtintegrating both the…

Q: 1. Find the general solution of У"-Зу'— 4х? —2у

A: See the attachment

Q: 4. Find the solution of the IVP y" – 4y' — 12y = 3e5x, y(0) = 18 7' y' (0) = -1/₁

A:

Q: Find General Solution of y" + y" = 0.

A: Given the differential equation is y"' + y" = 0. Here the auxiliary equation is m3 + m2  = 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.