y" + 7y + 6y = 0 %3D

Q: y' + 2y = e*,

A: Note: Since you asked multiple questions, I solved first one if you want answer of other questions…

Q: w = 4x + y² +2²³₁ x = ers²₁, y = 1 y = In(r+s).

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Q: (2x – 5 y dx + (- 5.x + 3y² kdy = 0||

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Q: Solve (x + y)² dy = a

A: Topic- Differential Equation

Q: y" + 2y' +y = e-*

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

Q: y (4x + y) dx – 2 (x² - y) dy 22 + x + 2 ln y = C ans.

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Q: メyゴ= ザ+×x。+y %3D ind gen eral solution

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Q: Simplify

A: Given: To simplify the expression       (2x2 y-5) (6x-3 y)…

Q: dy ニ 3 x +y-2

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Q: •3 fx(2-x) 10. dy dx 0. r2VIn 3 VIn 3 35. •VIn 3 et dx dy

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

Q: y² (y + 2)ï dy

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Q: 2y dy y + e

A: ∫e2y7+eydysubstitude u=7+ey→dudy=eydy=e-ydue2y=(u-7 )2 ⇒∫(u-7 )2udu⇒∫(1-7u)du⇒u-7ln(u)put…

Q: y = x(2x+1), y" y = (4x − 3)¹/²2, d³ y dx³

A: Topic:- derivatives  Note :- as per our guideline if more than one question uploaded than only first…

Q: 2x°dy = y(2x² + y²)dx

A: Differential equations

Q: d?y Calculate dx2 y = e-X + eX d?y dx2

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Q: dy=y°-1 ex 2y

A: This is Separable differential equations

Q: Y = 4x²-5 Vsx dy=?

A: We want to find derivative of y, The given expression for y is,               y=4x5-55x

Q: 1. S+1)dy y2+4

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Q: V16-y? /32–x²–y² V 22 dz dx dy

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Q: (x² + y2) dx dy ow urves y = x² and

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Q: dy Differentiate implicitly to find 6 5 3) x y+9x = 6y +4 dy

A: A detailed solution is given below

Q: -dy (49 – y2 )

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Q: 3y 6. S dy y-3 7. SVIV7+xVx dx 8. S dr V1+r3

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Q: S1? SoY So *y xyz dx dz dy X-y

A: Consider the given triple integral as, I=∫12∫0y∫0x-yxyzdxdzdy First of all, we have to identify the…

Q: dy 34. = ty² +3t²y with y(-1) = 2 %3D dt

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Q: d?y dx2y =0 with initial conditions y(0) = yo and y - 0 as x oo,

A: We have to find the solution of the following differential equation.

Q: eY+Ve2y-4 5. x = In sove for y“ 2.

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Q: 2) dx dy x²+y² 2хy ||

A: Integrating the given equation.

Q: d ?y + 5 dY + ol x2 6X=0 dx

A: This is a basic differential equation question

Q: 7. y Vzy dz + dy = 0

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Q: ed by F(x, y) = (-: %3D

A: The function given is , F→x,y=-x,y. Draw the table for the points plot on the graph for the vector…

Q: d²y + y = 0 dx2

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Q: and Y=-2 when X=Z dx

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Q: Find the antiderivative dx/(x2+4)3

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Q: ſx = s² – t² . z = 2x – 5y, ly =s•t³ · t3

A: We find complex function

Q: (yæ² + æ*) dy – (y³ + 2 y² a 3 3 y x²) dx = 0 - - –

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Q: y(a² + y² )dx – x(x² – y² )dy = 0 %3D

A: Given: yx2+y2dx-xx2-y2dy=0

Q: x, y) Edy is

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Q: y2 dy + y132x %3D dx

A: Given

Q: Solve the D.EXY+Y=1/1/2

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Q: 1 y2 y3+3 dxdy 0 0

A: Let I=∫01∫0y2y3+3dxdy

Q: C:y 2x, x 8 ing (x² + y³)dx + (2xy +3)dy1

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Q: ' + y = y? Py = 1 + ce¬# Dy-1 = 1+ ce¯ Py = 1 + ce² Dy-1 = 1+ ce

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Q: 16. (2+) y dy

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Q: Solve for the General Solution. ( x csc y/x-y) dx + x dy = 0

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Q: dy y2+1

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Q: y² (y + 2)ã dy

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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.