d²y 7. – 4y=-6e', y(0)=3; y'(0)=4 di? 2/2

Q: Z4 =:₂₁ (4x²yz - dz dy dx S₁

A: Given ∫23∫-14∫104x2yz-z44dz dy dx ∫23∫-14∫104x2yz-z44dz dy dx=∫23∫-14∫104x2yz dz dy dx -…

Q: (3y + 2x) dx –x² dy = 0, given that x = 1, when y = 2

A:

Q: 5. Find dy/dx (y - x)? = 2x + 4

A: Given: y-x2=2x+4 To find dydx. Solution: Power rule of differentiation states that: ddxxn=nxn-1…

Q: Vx 3 1- evNīdy dx - 3 y3 e*y dx dy

A:

Q: 16 4+x² dy when y = Find 4 – x² dx dy dx

A:

Q: Solve for the general solution of (ylny-e^-(xy))dx+(1/y+xlny)dy=0

A:

Q: Solve the initial value prol dy + 8, y(1) = 3 dx y%3D 4 Jx +8x 19 4 Oy=Vx + 8x - 6 Oy=-- - 8x- 6

A: Explanation and solutions is given below....

Q: 7. Solve for dy/dx if x = 2 + t and y = 1 + t2

A: From the given problem: x=2+t;y=1+t2 As we know that the Power law: ddxxn=nxn-1 We know that:…

Q: 2 dx + ( 2x-y+3) dy = 0 ans. y + C = - In |2y-y+4|

A: See the details solution in below

Q: dy| 2х — 6 - Find- , where y = dx\x=1 x + 2 Enter the exact answer. dy dx=1

A: Solve

Q: 18. S V1+x dx 1-х

A:

Q: Z4 e: 2₁₁ (4x²yz - ) dz dy dx 1 4

A:

Q: Find the particular solution for (2y3 – x³) dx + 3xy² dy = 0 when x = 1, y = 1

A:

Q: dy + 0.4ty = 3t dt with y(0) = 5.

A: This equation is of the form of bernoulli equation.

Q: (Зх — у — 4)dy — (х + у— 4)dx %3D 0 - -

A:

Q: 2) If y= 3x- 2x and clyldt = 3 1. Find dx/dt when x= 2

A: Given that: y=3x2-2x and dydt=3

Q: dy In |= 8x+7y; y(0)=0 dx

A:

Q: 25. (ye*" – 2y³) dx + (x e*' – 6xy² – 2y) dy = 0; when x = 0, y = 2. ANS. e* = 2xy³ + y² – 3.

A:

Q: If y = e Oe3 Oe 3x X² O 2e3 O 3e³ then dy dx at x = 1 is

A: To find derivative of given function at x=1

Q: 2x(y + 1) dx – ydy = 0 when x = 0, y = -2 %3D -

A: Here differential equation is given as 2xy+1dx-ydy=0or2xy+1dx=ydy⇒2xdx=ydyy+1⇒2xdx=dy-dyy+1

Q: 8. 5x* + -- * ) dx +2 (x³ + In x – e*) dy = 0; y (1) = 0 %3D

A: Differential equation solved by using integrating factor

Q: 17. (Vx-x)dx (1-x²) dr 18. 19 o. Sy² dy 20.

A: Given problems:-

Q: dy 3 sinh y - 5 cosh y

A: Given, I=∫dy3sinh y-5cosh y

Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: dy 5. S: y(1-Vy)2

A:

Q: O Calculate ........... 2 4-y2 dy dx O I-X ® yde dy

A: Here we will find the solution of question 4. a)∫01∫1-x1-x2dydx Solution: Here the independent…

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

A:

Q: у (9х — 2у) dx - x (6x = y) dy = 0 -

A: Given:- y (9x - 2y) dx − x (6x — y) dy = 0 To find:- Solve given differential equation when x=1, y=1

Q: By?dx +[2yłn () + 3siny dy 0 ;when x = 1, y = 0 ²+3x x+3

A:

Q: 13. dy/dt = y²(1-y)², -∞ <yo <∞

A:

Q: 9. Find the General and Particular solution of = 4y ; y= 3,when x dx

A:

Q: Cln S iny 7. ex+y dx dy 0.

A: I=∫1ln8∫0lnyex+ydxdy⇒I        =∫1ln8ey∫0lnyexdxdy               =∫1ln8eyex0lnydy…

Q: y et 2x *Sec2X Pinel dy o

A: By using these differential formulas that are ddxex=ex, ddxax=axlnx where a is constant,…

Q: 9. If dy = xy² and if y = 1 when x = 0, then when y = 3, x is equal to dx 0 -0 DIE

A:

Q: 17 (7+ x²^ dy when y = dx Find %3| 7 – x²

A:

Q: 4. if x^3+y^3=2 find the value of (d^2y)/(dx^2) at the point (1,1)

A:

Q: dy/dx 5 - y = In(x – Vx²+ 1)

A:

Q: 4. ydx + x(Inx - Iny - 1) dy = 0, when x = 1, y = e

A:

Q: dy dv 2 Find for y = = [ √3 +4 dt. 0

A:

Q: 3. a) If y = 6x - 5x +7x +2x – x+10, find dy at (2,3) i. dx d'y il. -at (1,-5)

A: See the attachment

Q: 9-y dy 5. S y

A: We will use trigonometric substitution.

Q: (4x + 3y – 7)dx + (3x – 7y + 4)dy = 0; when x = 1, y = 1

A:

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

A:

Q: 9. S(9 + 8y – y²)? dy 10. S (e*–2)² dx e 2x + 4

A:

Q: 26. = 2xy² + 3x²y², y(1) = -1 dx dy 27 -7

A:

Q: 5. Solve d'y+dy =5 with y"(0) = 0, y'(0) = 2, di dt y(0) = 0

A:

Q: dy 3) xIn x- +y = 2 In x dx

A:

Q: Can you help me step by step?

A: Let u=1+x^4

Q: Find dy/dx by the implicet differentiasion x2+y2=64

A: