d²y 10 9y = e3x + sin 3x dx2

Q: y" – 4y' + 4y = 2.x² + 4xe²" + x sin(2x)

A: Given differential equation is

Q: ● √3x dy dx √x² + y² So So

A:

Q: 5. Solve d²y dy dx² dx +2 + 5y = sin 2x, given that y(0)=3, y'(0)=0.

A:

Q: d²y + 4y = x² sin 2x dx2

A:

Q: 3 2 2. (2x + 3y' )dx + 9xy'dy = 0 dy 3. Sin 2x dx 2y 2Cos x

A:

Q: G3- y²sinx+3e3*)dx+(3xy² +2ycosx+)dy=0 |

A: In this question, we have a differential equation of the form Mdx+Ndy=0 Here we have to check the…

Q: 2. 6y dx- x(2x' + y)dy = 0

A:

Q: √ ² S ² (2y² + x² + 3) dy dx 0

A: Given integral, ∫02∫012y2+x2+3dydx The objective is to evaluate the integral.

Q: Find d²y/dx². y=xsin x 10 cos x

A:

Q: 3. dy = (x - 3y)dx ans. 9y = 3x - 1 + ce 3

A:

Q: 2.) 2 (x -y)dx + (3x² - GxY - 2x) dy

A:

Q: 7. (2x + 3y)dx + (3x + 2)dy = 0 When: x = 3, y = 2

A:

Q: (3x + 2y + 7)dx + (2x – y)dy =0

A:

Q: 2. (6x2 - y+3)dx+ (3y2 – x- 2)dy =0

A:

Q: dy 6y = 12x- 50 sin x dx² dx

A:

Q: 2x+2 dx. 5. x2-2x+1 dy 6. 5. if y = (1+ x²)etan-1x

A:

Q: Find dy dx dz 2 9=(z-3 Inax) a = constant

A:

Q: find (d^(2)y)/(dx^(2)). y=xcos(5x)-sin^(2)x

A: y=xcos5x-sin2x Differentiating with respect to x, we get…

Q: 3) (2xy – sec²x)dx + (x² + 2y)dy = 0

A: Given :           The differential equation is 2xy - sec2xdx + x2 + 2ydy = 0

Q: find dy/dx 3x² +5y'x² +4/y, a) x² +4x,/y-5y² = 3 (ans.: 2x 10x'y- Jy

A:

Q: dy 4.x+ (4x² – 1)y = -3 sin(2x) dx dy dx²

A: In this question, we find the normal form of the differential equation and then solve it.

Q: (3x+2y+7)dx + (2x-y)dy=0

A: Given differential equation .3x+2y+7 dx+2x-ydy=0We have to solve the differential equation .

Q: d²y 2x(1-x)+(5-7x)-3y=0 dx dy dx

A: To obtain the power series solution of the second order differential equation, use the following…

Q: (6e² + 6z+4 cos z+2)dx %3D

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: dy 5 (ӕ — 2) уї %3D dx x-2 నా

A: NOTE: Refresh your page if you can't see any equations. . .............(1) substitute…

Q: Solve x3sec2y dy/dx+3x2tan y=cos x

A:

Q: (x +2y)dx - 3y dy =O

A: Given differential equation is homogeneous differential equation which can be solved by doing the…

Q: [2x*yžcosx² – 2x*yå + x/5]dx + [x/5stnx² - x° /9]dy = 0 3 2x²yz + x [x/ysinx? – x³ /y]dy = 0 -

A:

Q: 2.2 (x²-y² + sxy + 2) y.dx + ( x + ² + 4xy + 2)x.dy=0

A:

Q: Solve (1+2.x) dy d²y -6(1+2x)- dy -16y = 8(1 + 2x) with y(0) = 0, y'(0) = 2. dx dx?

A: Given differential equation is: (1+2x)2d2ydx2-6(1+2x)dydx+16y=8(1+2x)2 Given differential equation…

Q: 3 7x + 6x - 5x dy find dx - Example 28. If y = 4

A:

Q: d²y dy - 6y + = 12x - 50 sin x %3D dx2 dx

A:

Q: d²y dy + 3x+y = 4sin (In(x)) dx²

A: Given Euler differential equation is: x2y''+3xy'+y=4sin(ln(x)) Let us take x=ez Replace:…

Q: +y² = 1, y(0) = 4 dx O 3 y2 = 1+7e 2 3x O 3 y2 = 1+7e 3x 2

A: detailed solution is given below

Q: 2 ГБА 0 4 - x - y dy dx

A: ∫01 ∫024-x-y dydx

Q: 4) [cos(2y) – 3x²y²]dx + [cos(2y) – 2xsin2y – 2x³y]dy = 0

A: Exact Differential equation

Q: dy 6-x.-3y= x' dx

A: we are given an ode -x*dy/dx -3y=x2 we have to solve this ode as we can see, this is a linear first…

Q: (x - 3y + 3)dx + (3x + y + 9)dy = 0

A: On solving this we will get

Q: (x-3y+2) dx +(3x+ 9y-12) dy -o 3.

A:

Q: (x-2y++)dx + ( 2xーy+2) dy =o 2. ー1

A:

Q: 1. fx³e*/2dx /4 2. S*x sin 2x dx

A:

Q: 2. (бх * у) ӑх *у (2х- Зу) dy - 0 3. (2xy– 3x²) dx + (x² + y) dy = 0

A:

Q: 7. (у — 2) dx + (3x — у) dy — 0. ANS. 12x = 3y + 2 + c(y – 2)-3. -

A:

Q: (メ2メ+Sx )dx h- Cos3x dk 120 x3-XSinx+ CusX dx C. 130 x41 (2メーリdy

A: As per our policy, I can only provide you solution for first three parts, but part (c) is not clear…

Q: y" – 10y' + 34y = 3x2 + x – 1 || | (D² – 10D + 34)y = -cos3x

A: 1-D-1 = 1+D+D2+D3+.... Note : As per our Guidelines, we are supposed to answer first question.

Q: d²y dy 3- 4y = 3e¬* dx x- - dx2 -

A: Given differential equation is

Q: (3xy³ + 4y)dx + (3x²y² + 2x)dy = 0; when x = 1, y = 1

A:

Q: d³y d²y +6 dx3 dx² dy -+ + 11 ax+6y = ex + cosx dx

A:

Q: 2) (3x²y – sin y)dx + x(x² – cos y)dy = 0 |

A:

Q: 2. メ +ッ 2. dy- X. dx

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.