y' - 5y = -xy, y(2) = 1

Q: Solve the differential equation dydx = 5cos(x)y

A:

Q: (x3 + ) dx + (y² + In x) dy = 0, is exact differential equation.

A:

Q: Use undetermined coefficients to solve the differential equation y"" -y=e¹- x + 16.

A: We have given a differential equation ,  y''' - y = ex -x + 16 First we will find complementary…

Q: The Bernoulli's form of the differential equation 2x³dy-− y(y² + 3x² ]dx = 0 is

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: The solution of the differential equation=1-x+y-xy is: dx

A: To solve the given differential equation

Q: 2 (y+ 1) da- ydy = 0

A: Explanation of the answer is as follows

Q: Solve the differential equation. xy' + y = 4Vx

A:

Q: find the solution of differential equation y' = 1+ e*-y

A:

Q: The solution of the differential equation In(y')=2x-y is given by

A:

Q: Solve the differential equation x y' = In x-3xy with initial-value y(1) =2.

A:

Q: 5. Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y )²

A: We have to evaluate: (y(x) + 1) ( d^2 y(x))/( dx^2) = (( dy(x))/( dx))^2:Treating y as the…

Q: find the general solution of the first-order linear differential equation. y' − (ln x)y = xx

A:

Q: determine the general solution to thegiven differential equation. y′′′ − y′′ + y′ − y = 0.

A:

Q: Find general solution of the Euler differential equation x2y” + 3xy’ - 3y = 0

A: x2y” + 3xy’ - 3y = 0

Q: Show that the function  y1=x-1 is a special solution of the differential equation y'=1-(y-x+1)2 and…

A:

Q: Find the general solution of the first order differential equation 2xy(dy/dx)=x2-y2

A: The given differential equation is a homogeneous. See attached file for a step by step explanation.

Q: What is the particular solution to the differential equation with the initial dx condition y(-2) =…

A:

Q: xy"+y'=0; y1=ln(x) How can this second-order differential equation be solved by general solution?

A:

Q: Solve the 1st order differential equation y3+x-1 y = x dx

A: Given differential equation is y3dydx+x-1y4=x. Note that the differential equation is of the form…

Q: (c) y' – y = e2=

A:

Q: The equation x² + e¤y = c defines an implicit solution of the differential equation

A: We have to differentiate the given equation with respect to x first.

Q: (c) y' – y = e2¤

A: We have to solve

Q: Solve for the General Solution of the given Differential Equation y' = y – xy³e- -2x

A:

Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

A:

Q: Find the general solution of the differential equation. y′ = ln x

A: The given equation is y'=lnx   By parts rule used: ∫udv=uv-∫vdu

Q: Solve the differential equation y" - 3y +2y cos(e-*)

A: This is a Non-linear differential equation. Which I have solved by operator method. See the solution…

Q: Find the solution for the second order differential equation y-4y = x sinh x.

A:

Q: y"- by! + gy = e

A: We have to solve the differential equation…

Q: What is the linear differential equation of the bernoulli’s equation dy/dx-y[1/(2x)]-y^5=0?

A:

Q: y" - y = e2* – sin x

A: To find the general solution of the given differential equation

Q: 2ydx = (x2 – 1)(dx – dy)

A:

Q: Find the general solution of the first-order linear differential equation xy′ + y = x2 ln x for x…

A: The first-order linear differential equation ,  xy'+y=x2lnxfor x>0. Solve the equation for the…

Q: y+ e*y= e*y²

A: Given differential equation is : dydx + ex y = ex y2   ⇒ dydx = ex (y2 -  y)   We will use…

Q: Find

A:

Q: 2) x – 1 = - 2e-y

A:

Q: Find the differential equation by eliminating the arbitrary constant  x2-y2= 0

A: To find the differential equation x²-y²=0

Q: Find a single solution y(t) of the differential equation y′′=2

A: A differential equation can be solved using the variable separation method. In this method, the…

Q: find the solution of differential equation y' = 1+e-y

A:

Q: Obtain a linear differential equation with real, constant coefficients that is satisfied by the…

A: If the particular solution is: y=2excos3x                                        ....(1) The first…

Q: y = 2 -[(1+y(t))sin tdt.

A:

Q: Match the differential equation with its solution. y' - 4x'y = x3 %3D

A:

Q: Solve the differential equation. xy' + y = 7Vx

A:

Q: 2. Solve the differential equation- + x, with y(1) = 1.

A:

Q: y' + xe*-y = 0

A: To Obtain the general solution of the Differential Equation

Q: Solve the given differential equation by variation of parameters. x²y" + xy' - y = In(x) y(x) = ,X >…

A:

Q: Find the general solution to the non-homogeneous differential equation. y" - 3y' = sin(3x)

A:

Q: y = ry' – In (y')

A:

Q: Determine an appropriate substitution and then solve the differential equation. xy' = y In(xy)

A:

Q: Use variation of parameters to solve the differential equation: -2x y" + 4y' + 4y : In x. = e

A: Here I am attaching image so that you understand each and every step.

Q: Use a substitution to solve the nonlinear differential equation: (y + 1)y" = (y ')²

A: Let y' = t Then , y''=dtdy  to find the value of y, integrate y' =t⇒∫dy =∫t. dt⇒      y =t22  So the…