(b) Use the substitution u = x In y to solve the equation (xy + 2ry ln² y + yIn y)dr + (2x² In y +1)dy = 0.

Q: y = (r² + 4r) e"

A: given question is solved with the help of product rule of differentiation    i.e. (f.g)' = f*g'+…

Q: for

A:

Q: Solve of the following Clairaut equation y=((x+4)y')+(y')^2

A:

Q: Solve for y in two ways. y' - 5y = -3

A:

Q: Solve: y''' – 3y'" – 6y' + 8y = 0 %3D y(0) = – 6, y'(0) = - 12, y'"(0) : - 54 %3D y(t) =

A:

Q: = sin(5x) for y(0) = 2

A: the solution is, y = (11 - cos5x)/5  The detailed solution is as follows below:

Q: Solve: y" - 2y' = xe 4x

A:

Q: y = In( sech2x)

A: The objective of the question is to find the derivative of the function y = ln(sech^2(x)).

Q: Solve: x²y" + 3xy' + 10y = 0

A: Solve 2nd order linear differential equation by let x=e^z

Q: Answer: y = -(e-x + c)/(1 + x2)

A: Given differential equation is,

Q: Solve: x⋅dx/dy​−y = x2sin(x)

A:

Q: Solve cosh(z)=1/2

A:

Q: Solve 2x'4 2xg+y'=2x +24

A: The solution are next step..

Q: Solve x'y-5xy+13y-0

A:

Q: Find the value of x'+7x-x+16, when x 1 + 2i.

A:

Q: Solve :     x²y"-2x(1+x)y'+2(1+x)y = x3

A: Given: The second order differential equation is x2y''-2xx+1y'+2x+1y=0

Q: Solve dy 2-x -subjectto y(1) = 0 dx ху

A:

Q: Solve xy' (2y -1) = y (1 - x)

A: We can solve the given differential equation by using the variable separable method.