3. x'sec'ydy – (1– 2x²tany)dx = 0 4. dy – (x - y + 1)°dx = 0

Q: syidr + [2yłn () + 3siny]dy: 6. x²+3x 3y?dx 5x ;when x = 1, y = 0 x+3,

A: Given, Differential Equation:  3y2x2+3xdx+2y ln5xx+3+3 sin ydy=0when, x=1 and y=0 To find: The…

Q: - y' = y – xy³e-2x

A:

Q: a) (e" +1) e*dx + (e* +1)"e*dy = 0 1 1 dy +y dx dy y? -1 c) dx x -1 si y (2) = 2

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Q: 10. 2ste tds +(s²e-t - t)dt = 0

A:

Q: y = Ce2*cos3x + C2e2xsin3x

A:

Q: y = C¿e* + cze¬× + 3x

A:

Q: 4. (y' — 5у) %3 х?е* — х е5x

A: According to question, Given differential equation, y'-5y = x2ex-xe5x.

Q: • / = Ity

A: y'=x-yx+y It is a homogeneous differential equation. Put, y=vx⇒y'=v+x·dvdx Therefore,…

Q: cQl Solve the differetial equat'ron Sin (2x)+ 5 Sin(2x)+ 3 eos (20)

A: As per the question we are given a linear non-homogeneous second order ordinary differential…

Q: (2xy + x)dy – [x² + y² + y + 1]dx = 0 When:x = 1; y = 0

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Q: У(ху + 1)dx + x(x'у? + ху + 1)dy %3D0

A: Given the differential equation is          y(xy+1) dx + x(x2y2+xy+1) dy = 0.

Q: 2y1 + x* JF }ix + (x*Jy + 2xfky = 0

A: Recall: If the equation is of the form  Mdx+Ndy=0. First , check the condition of exactness  i.e,…

Q: Solve the following differential equations: 1. y(lnx - In y) dx = (x ln x - x ln y - y) dy

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Q: y" – 4y – 5y = et + 2x

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Q: g. A thermometer reading 50°C is taken outside where the temperature is 30°C. Five minute later the…

A: Consider temperature of thermometer after 't' minutes is given by T(t), then from the given…

Q: = 2x- y dx

A:

Q: d?y + 4 + 4y(t) = 2e-tu(t) , y(0) = 3, y(0) = 0 dy dt2 dt

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Q: Solve the following differential equation: yde+xdy 1-x²y² +ædr=0. = constant.

A: Given that the differential equation ydx+xdy1-x2y2+x dx=0

Q: Question 11 (D² - 3D + 2) y = 4x²

A:

Q: y" + 5y/ – 6y = e2® - y = C1e6 + C2 e" + 4 y = C1e-6z + C2e" – e2 | 8 y = C1e6# + C2e¯* + 8 y =…

A:

Q: d²x dt² solve for x. 2 + w³²x = F sin wt

A: Given differential equation isd2X/dt2  + w2X = F0 sinwt

Q: y У — х. y' = 2+ sin

A: Given y' = yx + siny-xx    ---(1)