If Y(x) = 5x is a particular solution for x'y" + 2y' = h(x) then h(x) = %3D %3D %3D A. 80x* В. 140х* C. 4x5 D. 70x* E. None

Q: Find y'. y = (4x° + 9) (2x7 - 4) OA. O A. 80x° + 126x° – 48x O B. 16x° + 126x° – 48x? O C. 16x° +…

A: y = 4x3 + 92x7- 4y' = ?

Q: Each of the following equations represents a cubic function

A: Given data: The first equation is y=2x2+3. The second equation is y=-x1/2-1. The third equation is…

Q: y” – 10y’ + 25y = 30x+3

A:

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

A: We will solve the problem

Q: Obtain the general solution. 1. (D^4 - 5D^2 - 6D - 2)y = 0 2. (D^2 - 2D + 2)y = 0

A:

Q: (3y" + y'-14)=3*256e768x - 1536

A: The given differential equation is  (3y" + y'-14)=3*256e768x - 1536

Q: Determine all solutions. y'= (x-y + 3)²

A:

Q: Eliminate the arbitrary constants of the equation y = Cje 2x + A y" - 2y' - 3y = 0 B y" - 4y' - 2y =…

A:

Q: ∫ln(7)0∫ln(7)0e^−(2x+5y)dydx

A:

Q: If f'(x) = and f(0) = 2, then f(4)can be written in fully simpi %3D S(x)

A:

Q: у"" - 8y" + 41у'- 234 е 3х, у"(0) %3D 187, у'(0) 3D 29, у(0) 3D 10 3x.

A: Now we solve this below

Q: 5+2x+x2 Find y' if y = 2x 243x/2,3x -1/2 -1/2 1/2, 1/2

A: Topic-differentiation

Q: S ( (24 + حمد ذا مرند

A: The given integral

Q: y^(5)−4y^(4)+4y^(3)=0 Use lower case c1,c2,c3,c4, and c5 for the arbitrary constants. y(t)=

A: y^(5)−4y^(4)+4y^(3)=0Use lower case c1,c2,c3,c4, and c5 for the arbitrary constants.y(t)=

Q: Check whether the given first order linear diff equation is homogenous or exact or separable or none…

A:

Q: y' =xy

A:

Q: 2x5y ' = y(3x4+y2)

A: For the solution follow the next step.

Q: Differentiate. y = In (4x² - 7x+9) y'=0

A: The function is The aim is to find the derivative of the function

Q: (с)(2у) dx + (6x3— ху — х)dy 3D0

A:

Q: 2- Solution of the following function {(dy/dx)-(cotx) y=(csc x)y³ }

A: The differential equation is given as dydx-(cot x)y = (csc x)y31y3dydx-1y2cot x = csc x…

Q: 31. Solve: x dy+ y dx = 4y dx * O x^4 + cxy 0 O y^4+ xy c O x^4 + xy = c О у4+ сху 3D 0

A: Topic = Differential equation

Q: 2x+5 dx = AV7- 6x - x2 + B sin - (**)- 1. Vア-6xーx2 +C

A: ∫2x+57-6x-x2

Q: For each of the following y, find the d^2y/dx^2

A: We know, d/dx (xn)= nxn-1, for any real number n. d/dx(u(x)v(x))= v(x)*d/dx(u(x))+u(x)*d/dx(v(x))

Q: Find y' y = 3x-2 2x+3

A: Given Functiony=(i) (ii) (iii)

Q: If y = (x+1)/(2x - root x' then y' will be?

A:

Q: Verify that y = Ce^−3x is a solution to the ODE dy/dx + 3y = 0, where C is an arbitrary constant.

A: Step 1:The provided ODE is:dxdy​+3y=0   .........(1)It is needed to verify that y=Ce−3x is the…

Q: 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x) | |

A: See 2nd step

Q: y₁' = -3y₁ - 4y2 +5et y2' = 5y1 + 6y2-6e¹ dan diketahui yı(0) = 19, dan y2(0) = -23,

A:

Q: Find the particular solution for ysqrt(1-x^2) * y'-xsqrt(1-y^2)=0  when y(0)=1

A:

Q: Find y' if y = (2x + 1) (4x – 1)². %3D

A:

Q: V24x'y³ • J50x² y° V40m²n • V50m n V28.x*y" 7xy 4 V42 75.xy* V3x 5. 3. 4.

A:

Q: 1−xy)^−2dx+[y^2+x^2(1−xy)^−2]dy=0;y(2)=1

A:

Q: Evaluate y'- 5y = 3e^x - 2x + 1

A:

Q: 10. y'+y = 3x³ + x; y(-1) = 4 су 3 3х3 + х; у(-1) %3D4

A:

Q: xcsc {( 2 ) - »]dx + y y dx+xdy=0 X (x² − xy + y²)dx−xydy=0

A:

Q: 1 = felan(4x*). sec²(4x²)xde 2

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.