y' – y2 – e3xy2 = 0 → y(0) = 1

Q: • / = Ity

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

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

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Q: 2x dy 2х. -y = x² - x; y(4) =2 dx

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Q: xdy − ydx + x³dx = 0

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Q: Solve the following differential equation d²y dy 2 + 5y = 0 - dx? dx subject to the following…

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

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Q: 3y"-Gy'+6y by = = e sec x

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Q: 1 -1 cost e' sint X' = X+ Use the method of Variation of Parameters. 1

A: we have, X'=1-111X+costsintet Consider the matrix A=1-111 and ft=etcostetsint First, solve the…

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: 1 1 7. The system X' = 0 2 3 X+ -2 4t e Use the method of Undetermined Coefficients. 0 0 5 2

A: The given System: X'=111023005X+1-22e4t     →    eqn 1 Where X is a general solution of the system.…

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: 4. t dv + (v – v² ln t)dt = 0

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Q: 手u等() dy dy seex dy-o 2 csey dx+ secx dy-o

A: