5. Find the general solution of (D³-D)y=4e*+3ex. Ans. y=2xe*+(1/2)e2+c1+c2e*+c3e*

Q: 4. (15pts) Identify (write down) the type of DE, and find the general solution. (y – 3x)dy = (x +…

A:

Q: ) Solve the initial-value problem dy :-2y 2x* ;y(2) = 8 %3D x- dx

A: We have to solve the given differential equation using the initial condition. Rearranging the…

Q: 1. Solve Cauchy-Euler equation. r²y" – ry' + y = 2x

A:

Q: 23. Find the particular solution that satisfies the initial condition. y'+ 3x²y = 3x, Initial…

A: The answer is given below:

Q: 6. Find (0) for a solution (x) to the initial value problem (secx)dy = 2√y+Idx; (n) = 3 2 3

A:

Q: 4. xydx + (y √ x² + y²-x²) dy=0

A:

Q: 2. Find the general solution of the first-order equation dy _ y² – 2ry dr

A:

Q: 2. Find general solution of the DE y" + 3y" + 3/ + y = 0

A:

Q: 3) Find the particular solution of the DE y" = 12x² if y(0) = 1 and y'(0) = 2.

A: This is a problem related to differential equation. Please follow the procedure given below.

Q: 2. Find the general solution to d²y dz² dy + 3y = e* dr

A:

Q: Determine the General Solution of ye2x dx = ( 4+e2x %3D ) dy

A:

Q: The solution of the initial value problem dy - -2xy, y(0) = 2 is %3D

A: We can solve this question as below

Q: 4) Find the solution of y'= 2(2xy) passing through (0,1).

A: Given, Equation  y'=2(2x-y) passing through a point (0,1).

Q: fin the general solution of (x+2y-4)dx - (2x+5-y)dy=0

A: Please see the below picture for detailed solution.

Q: Give the general solution of xy²dy = (x³ + y³)dx in explicit form.

A: Given differential equation is  which is homogeneous differential equation.

Q: If y = e2t is a solution to y" – 5y' + ay=0 then a=

A:

Q: 13.Obtain the general solution of y²dx+x(x +y)dy = 0

A:

Q: 19. Show that yı = 1 and y2 = /x are solutions of yy" + (y')² = 0, but that their sum y = y1 + y2 is…

A:

Q: What is the general solution of xydx−(x2+3y2)dy=0

A: Topic :- Differential equation

Q: Find the solution of the initial-value problem dy dy dr² 12y = 0, y(0) = 3, y/(0) = 5. dr

A:

Q: 23. Find the particular solution that satisfies the initial condition. y'+ 3x²y = 3x². Initial…

A: Particular solution is the solution which obtained by giving particular values to independent…

Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

A:

Q: 12. Find the general solution of x²dx + y(x – 1)dy = 0

A: This is a variable seperable DE.

Q: 3. Find the particular solution of the linear equation dy + -y = dr 1. if y(1) = 0.

A:

Q: Find a general solution of y"- iy'+6y= 0.

A:

Q: a) Give a particular solution for y" – 2y' + y = 3e*. %3D

A:

Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: Solve the initial-value problem d²y 4- - 4 - 3y = 0, y(0) = 1, y'(0) = 5. dx2 dy dx

A:

Q: y" + y" = 3

A: Solving the given third order differential equation

Q: 9. Find the general solution of y(2x + y²)dx + x(y² – x)dy = 0

A:

Q: Obtain the general and particular solution 4. xydx + (x² + y²)dy = 0

A: The given problem is solved below in detail.

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

A:

Q: 3. Obtain the general solution of: (x – y)(4x + y) dx + x(5x – y) dy = 0

A:

Q: 1. The complementary equation to dt² + dy + 4y = 5e-³t is:

A: Solution is here

Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

A:

Q: Find the solution of (1 + e²)yy = eª that passes through (0, 1).

A: (1+ex)yy'=ex(1+ex)ydydx=exseparation of variablesydy=ex1+exdxIntegrating both…

Q: Find the solution to the initial value problem. y'(x) = -y+ 2, y(0) = -2 %3D

A: Here, the given differntial equation is: y'(x)=-y+2...(1) with the initial value y(0)=-2

Q: 6. Find the general solution of 2x(3x + y – ye-**)dx + (x² + 3y2 + e-**)dy = 0

A:

Q: 5- The general solution of the following equation dy d²x 10+ 25y= 0 is dx

A:

Q: Yp = Find a particular solution to y" + 5y' + 4y = - 19te³t.

A: Introduction: The differential equation has a particular solution, which is a singular solution of…

Q: 2. Obtain the particular solution. y"-y'-6y=0; when x=0, y=2,y'=1

A:

Q: Determine the General Solution of ye2x dx = ( 4+e2x ) dy %3D

A:

Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: 4. Find the complete solution of: y" + 4y' + 3y = e with y(0)=1 & y'(0)=0

A:

Q: 2. Find the general solution of d³y dy dy 6- dr3 + 12 dx2 dx 8y = 21e2 -

A: To find- Find the general solution of  d3ydx3 - 6d2ydx2 + 12dydx - 8y = 21e2x

Q: Show that xy – 2 = cxy is a solution of (x² + y2 – x)dx – ydy = 0.

A: Given  x2+y2-xdx-ydy=0 dydx=x2+y2-xy

Q: 4. Verify that y=cx+e² +1 is a solution of the equation y=y'x+(y')' +1.

A:

Q: Solve the initial value problem: d²y 2e-*, y(0) = 1 and y' (0) = 0 dx2

A: