Solve the given differential equation by separation of variables. ds ks = dr S =

Q: 10. 2ste tds +(s²e-t - t)dt = 0

A:

Q: 2ss" + (s')² = 0

A: we will solve the differential equation.

Q: 11. (2х — бу + 4)dx + (х — 2у — 3)dy — 0; when x — 1, у %3 1

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Q: 4. 2ydx + (x ay³) dy = 0

A:

Q: 4. (y' — 5у) %3 х?е* — х е5x

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

Q: Solve the given differential equation by undetermined coefficients. begin mathsize 16px style y…

A: The solution is shown below-

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: (e"siny + tany)dx + (e*cosy + xsec*y)dy = 0

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Q: 2x dy 2х. -y = x² - x; y(4) =2 dx

A:

Q: Consider the differential equation:=-y. If the general solution is y = cet ,cER, which one of the…

A: We can solve this as follows:

Q: 4xi4=*

A: Order :-The order of a differential equation is the order of the highest order derivative involved…

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: Find the differential equation given the general solution: y = cer + Czex + 3x

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Q: (2+x²)y" + xy + 4x²y <=0 Compute the recursion formula for the coefficients of the power series…

A:

Q: Use partial fractions to find the power series of the given function and find the interval of…

A: we have given a function f(x)=10(x2+1)(x-3) We have to use the partial fraction and then write the…

Q: dy 1. tanxsin2y = sin²x + cos²y - dx

A:

Q: y cos( xy)dx + [2y +x cos(xy)]dy = 0

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Q: d³u 2 dr5 d*u - 7- dr4 + 12 d³u dr3

A: The differential equation is given 2d5udr5-7d4udr4+12d3udr3+8d2udr2=0. Here ,s=ddr then equation…

Q: du х — у— 1

A:

Q: dy xy' = 6y + 12x*ys, (y' = dx

A:

Q: From the differential equation dy = x2 dx, what is the equation of y in terms of x as the curve…

A: Given: dy=x2dx

Q: Solve the given differential equation by separation of variables. dS dr = KS

A:

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: 4. t dv + (v – v² ln t)dt = 0

A:

Q: * + 10x + 21x = 0 x(0) = 4 x(0) = -3

A: