dy 1.xy? = y3 – x³, y(1) = 2 = y³ – x³, y(1) = 2 dx

Q: dy 3 y = x*y3 dx

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Q: dy 3. + + 2y + y² = 0,yı = -2 dx

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Q: 5 (x² + y² )dx dy -5 J –1

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Q: H2. 2dy dy dr2 d²y dy :1 at x = 0. dx – 52+2y= 2x², y=7 and - dx

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Q: Find dy/dx for (x+y)3=x3+y3,at the point  (-1,1)

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Q: 1. (x- v)dx+ (3x + y)dy = 0 when x = 2, y = -1

A: Let us first solve x-ydx+3x+ydy=0. So,            x-ydx+3x+ydy=0Let y be the dependent variable.…

Q: = y - dy 3. 25 @ y (0)=1, y (0) =2 dx2 dx

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

A: Solve

Q: dy is let y = ln(V – 9 + a). -9+x then dx S'

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Q: d'y dy +4- + 3y = 0,0 < x < 1; dx? dx y(0) = 1; y(1) = 2

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Q: dx 2. Find the value of at y=1 if x=z³+4z and z= (y² + 2y)²/³. dy

A: We have to use chain rule while differentiating.

Q: Dy/dx +(4xy^4)=0 X dy/dx-y=2x^2,y(1)=1

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Q: dy +xy 1-y, y(1) = 0 dx

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Q: dy Q2 Find dx of x = *-Y 2 x+y

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Q: dx 1. S 2x-x² dy 2. if y = x* (In x)? . dx 3. Sx³e-* dx .

A: We have to find the integration and derivative as asked in the given question.

Q: »4-x² 1-y- xe?y dy dx 4 - y (b) Ln(a² + y? + 1) d dy (a) 0, /1-y²

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Q: 2y (x+y+2) dx + (y²-x²-4x-1)dy = 0 when x=2, y= 3 |

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Q: 1. y (4x + y) dx -2(x²-y)dy = 0 2. (2xy4e + 2xy³ + y)dx + (x²y4ey - x²y²-3x)dy = 0

A: We have to find Solution for given D. E

Q: 2. ( 3 x - 3 y - 2) dx - (x - y + 1) dy = 0

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Q: +y Evaluate dz dy dx 20 3 0 -3 0 00 -10 -4 0 10 -2 0

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Q: x+y, 9- (e* + In y)dx + (- )dy = 0 y +(x* + y*)e°'dy = 0 10- x(1+e')dx

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Q: (2siny + 1)dy : 4 and y(0) = 5. dx What is x when y = x?

A: Given:  2siny+1dydx=4, y0=π2 Using Variable separable  2siny+1dy=4dx Integrating both sides, we get…

Q: dy 2. if y = In(x² + 1) Then at x=1 %3D dx 2- 2 In 2 2- 1 1- 4- 1/2

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Q: X ( CSC ( X ) - Y Inx- X y - y dx + x dy = 0 dy - (Iny - Xdx X

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Q: dy 1- dx e¯x-y-2 y(0)= -2 %3D dy 2- dx ylny %3D 1+x2 y(0)=e²

A: 1. ddxy=e-x-y-2,   y0=-2A first order separable ODE has the form of Ny·y'=MxRewrite, we get eyy'…

Q: solve x (dy/dx)=x^2y^3 - y, y(1)=1

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Q: d’y_2dy 3 y=2sin°(x) dx Determine the general solution of 2 dx

A: We have to determine the general solution of the differential equation…

Q: 5/xy dy -2, х, у» 0 dx y =

A: See the details solution in below

Q: 1 dy 2 - Y = 0 y =x*prove that - 2)- = 0 y dx

A: Given, y=xxTake log on both sides,lny=lnxxlny=xlnxDifferentiate on both…

Q: d²y dy + 0.6 + 8y = 0 1. a dx2 dx where y(0) = 4 and y'(0) = 0. Solve from y(0.2) if h = 0.2.

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Q: y 3) dx Ans: x = y ln y + 2y In y+y-x y

A: Exact differential equation: Any differential equation Mdx + Ndy = 0 is an exact differential…

Q: x' = 1 t + 8' dy 4e-21, dx x' = tsin t², = x(1) = 0 y (0) = 3 x (0) = 1

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Q: 23. dx + 4y = 0; y = cje2 + czxe2x dx d'y + 2x - x + y = 12x²; dy 24. x dx dx "dx y = cx- + czx +…

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Q: dy y-x General solution of = dx y+x

A: Solution:

Q: dy If y = x- xy +1, then when x = 1, is dx 2-0 2-2 O nonexistent 1/2 1/2

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Q: dy 2. dx = x³(y – x)² +, Y1 = x,x > 0 y У1 — х, х > 0 dy 3. + 2y + y² = 0,yı = -2 - dx

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: dy when x = 1 is dx If y = e-ª In x then A) 0 B) Does not exist D) = E) e

A: We have to differentiate the function y=e-x lnx Use the product rule of differentiation…

Q: d²y – 4y = 0 dy, - (at x = 0) = 4 dx а. dx? y(0) = 2; - d²y b. 5- dx2 sdy dy - (at x = 0) = 0 dx +…

A: To solve the given differential equations.

Q: dy 1 a) dx dy y=3+e dx 4

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: d²x = y² + 1 а. y dy2 y (* + - ** + 1 dx, 2 d²x x² + 1 dy² d's d²s С. dy3 dx? () = x² + 1 dp. d. y…

A: An ordinary differential equation is an equation involving only one independent variable

Q: dy 2 = 3, ,3 X'y' - xy dx

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Q: 2x - y + 5) dx - (2x + y) dy = 0 where x= 3, y=7

A: Let's find.

Q: (e + 1)'e-Y dx + (e* + 1)°e* dy = 0 ху + 3х — у — 3 dx ху — 2х + 4у — 8 dy

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Q: dy 2 The integrating factor of -y= 3x² is dx -

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Q: d²y dy 2. +4 + 4y = 0, when x = 0, y = 1, y' = -1 dx² dx

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Q: (y In y e") dx + +x In y dy = 0

A: The given differential  equation is of the form Mdx+Ndy=0. Identify the functions M(x,y) and N(x,y),…

Q: d²y dy dy %3D 1 2. dx2 6y = 0, when x - 0, y = 2, - %3D dx dx

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Q: 6. - ydx + (x ++ Jy )dy = 0 7. (1+x*)dy + x(1+ 4y°)dx =0 8. (e* + y)dx + ( 2+ x+ ye" )dy =0 2y 9. 4.…

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Q: d²y dy -2 +4y dx 2e 2x dx2 x3 an is given hy:

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