General solution: (D² + 1)y = sec³x

Q: Find the solution fo (x^3-y^3)dx + xy^2

A: Here we have,  (x3-y3)dx+xy2dy=0⇒(x3-y3)dx=xy2dy⇒dydx=(x3-y3)xy2 ..............(1) Which is a…

Q: 5) (x- 4)² + y² = 9 Center Radius

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Q: Find the general solution of y' = y secx

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Q: Solve using indeterminate coefficients y '' + 9y = x ^ (2) e ^ (3x) + 6

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Q: C has equation 2x2 +y2 = 18. Dete l passes through the point (1, 0). %3D

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

Q: dy りー! り(-)ニ。 x+3 2, xy' =1+X ら(4)=0

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Q: D3-7D² + 16D-12)y=e^7x + Cos5x + Sin5x

A: Given:

Q: (9x-4y+4)dx-(2x-y+1)dy=0

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Q: Solve (D2+2D+2)y=e-x+sin 2x

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Q: Solve (D3-3D2+3D-1)y=x2.ex

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Q: Solve using variation of parameters

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Q: Q2: solve the equation dx 2x dy y y 3.

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Q: 2xyy'=1+y^2 solve using separation of variable (diff eq) when y=3 and x=2

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Q: dy 15 +4y-042

A: ∫115+4y-4y2dy

Q: Solve for d2y/dx2 for x = u2 - 3 and y = 4u3 - 2u

A: Given x=u2-3 and y=4u3-2u. To find d2ydx2. Solution: We have, x=u2-3 Differentiating the given…

Q: lax +3y-5) dx + (3x-y -

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Q: solve: [Cax+3)*D²+6(2z+3)D +bJ y 18log (az+3) Answer 7 = fA cos (2243 alog caz+3) –4 +BBin/ x+3 22+3

A: It is an Cauchy Euler differential equation

Q: y" – 6y' + 9y = :

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Q: |2/2r| 2, dx -1

A: Let I is the value of given Integral.

Q: Solve y"-4y'+13y= yo)=-I ,y'co)=2

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Q: Solve the Solution (6x+y^2)dx+y(2x-3y)dy=0.

A: Given differential equation is in the form Mdx+Ndy=0 Where, M=6x+y2 and N=2xy-3y2 If ∂M∂y=∂N∂x then…

Q: Please solve (2x-y)dx + (4x+y-3)dy = 0 using Linear coefficient method.

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Q: y' = (4x + y)?

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Q: use Separation of Variables to find the general solution. y' = x sec y

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Q: 2 V4-x2 e*²+y* dydx =? -2 0

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Q: Solve (D2 - 6D + 9)y  = e2x + Sinx

A: The given differential equation is D2-6D+9y=e2x+sinx The auxiliary equation is D2-6D+9=0 Solve for D…

Q: Solve using method of variation of parameters: y" + 2y' - 8y = 2e-2x - ex, y(0) = 1, y'(0) = 0.

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Q: Q3/ Solve dy dx4 2d²y + 1 = 0 dx²

A: Given d4ydx4-2d2ydx2+1=0To find solution:

Q: Evaluate d2y/dx2 at the point (0, -9). x = t3 - 3t y = 3t2 - 9

A: Given: x = t3 - 3t y = 3t2 - 9

Q: Solve rue I.v.P. ý + 3y'-s y = y co1=2 yco)=-3

A: Given,y(0)=2 and y'(0)=-3y''+3y'-5y=0    Integrating both sides y'+3y-5=C1...............(1)on again…

Q: 8.) Find of y3 = x* + 3x d?y dx2

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Q: Н. W.: -1/3 6dx 2. V9x2+ 1 c2/3 dy

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

Q: 4-y² ²) dædy 2 2

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Q: general solution of (D2-1)y=2/1+ex

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Q: Show complete solution. 6y^2dx-x(2x^3+y)dy=0

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Q: what is the solution of equation 2ydx + (2xlogx - xy)dy = 0

A: Given differential equation is. 2ydx+2xlogx-xydy=0

Q: What is diffential equation of y"-5y'+4 when y(0)=1 and y'(0)=1

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Q: Solve (D² – 3D – 4) y = 16x – 50 cos (2x)

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Q: y = e² -Vx sec 6x 3

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Q: If x3 + y3 = 16, find the value of d2y/dx2 at the point (2, 2).

A: Given:

Q: (D2+9)y=cos 3x

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Q: Solve: •2-3x 5² 5²-³x fx+y x dz dy dx 0 0

A: Here we have to evaluate the given Integral

Q: (62 - y+3) dz+ (3y2-a-2) dy= 0

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Q: Solve using variation of parameters: y" – 2y' + y = -

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Q: Solve using variaiton of parameter (D³ – 3D +2)y = (1+e2x)-1/2

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Q: Solve the simultaneous equations y = 1 + 3x – x2 and y = 3 – x graphically. %3D fom

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Q: Solve (D - 4D +4) y = 8xe2* sin 2x

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Q: (y2-2xy-x2)dx+(2x2)dy        Find the solution of the equation through the point (1,2)

A: We have to find the general solution from the given condition

Q: "+y = sec³ x

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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.