Solve the differential equation using Laplace transfom: y" - y' + 2y = t, y(0) = -1, y'(0) = 2 Where : L(y"(t)) = s²y(s) – sy(0) – y'(0) L(y'(t)) = s y(s) – y(0) L(y(t)) = y(s)

Q: y' = (y² - 1)(e-2) where, y(0) = 3 2 and y(0) = -4

A: Given: The  differential equation is y'=y2-1ey-2 and   y0=32 , y0=-4. Plot the graph of the solution…

Q: y²y" = y³(y')² – yy'

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Q: Solve the differential equation: 2cos(2x)y^2+2ysin(2x) dy/dx = 0, y( π/8 ) = −2, find y(t)…

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Q: Consider the nonhomogeneous differential equation 1 y" (x) + y(x) = e # +: sin a

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Q: The differential equation ty' = cos² (y) is . ...linear, separable, and autonomous. O.nonlinear,…

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Q: (B): Classify the following differential equation according to order, degree, and linearity (1): (1…

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Q: Assume that y is a function of x and use the integrating factor method to solve the differential…

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Q: Solve the differential equation y’=xsqrt(y); y(0)=1

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Q: Solve y" + 2y + 2y = e cos(x) with y(0) = y'(0) = 1.

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Q: Find a function y = y(x) that has all of the following properties: • It satisfies the differential…

A: We have to find a function y=y(x) that has the following properties. 1) It satisfies the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.