Find the solution r (t) of the differential equation with the given initial condition: r'(t) (sin 6t, sin 7t, 9t),r(0) = (2,2,3) r(t) = (

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A: We rewrite the differential equation as dydx=4y. Now dy4y=dx⇒∫dy4y=∫dx⇒14∫dyy=∫dx⇒14 ln y=x+C1⇒ln…

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Q: Solve the given differential equation with initial condition.  y' = 2y, y(0) = 2

A: given,             y'=2y       and y(0) = 2

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A: Given differential equation: with x=0, y=0. Used formulas:

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A: y'=cos5xy dydx=cos5xy dyy=cos5xdx y-12dy=cos5xdx take integration

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A: Please see the answer below.

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A: dydx=xey⇒dyey=x dx⇒e-y dy=x dx⇒∫e-y dy=∫x dx⇒-e-y=x22+C⇒e-y=-x22-C⇒-y=ln -x22-C⇒y=-ln -x22-C

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