Find an explicit solution y(x), by using the given substitution then solving a linear ODE. dy...

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Find an explicit solution y(x), by using the given substitution then solving a linear ODE. dy dx SOLUTION: The chain rule gives du dx dy dx dy dx + y = y³, y(0) X = X 1 du 3y² dx X −y=y=², y(1)=2. u= y³. 3y2 dy. So dy dx dx du dx 11. y=y=² du dx This can be solved by integrating factors. μ(x) = x-³, so (x-³u)' = 3x-4 + C So u = −1+ Cx-³, and y = (−1+ Cx-³). Solving y(1) = 2 gives C = 9. 3u 3 u=y=² ⇒>> + 2xy = xy², y(0)=1. u=y-¹. 1 du 3y² dx du X - 3y³ = 3, dx 3 X So U = U=X 3 X x20 2 dy + xy + y² = 0, dx y(1) = 2. u=y-¹. Find an explicit solution y(x), by using the given substitution then solving a linear ODE. dy dx SOLUTION: The chain rule gives du dx dy dx dy dx + y = y³, y(0) X = X 1 du 3y² dx X −y=y=², y(1)=2. u= y³. 3y2 dy. So dy dx dx du dx 11. y=y=² du dx This can be solved by integrating factors. μ(x) = x-³, so (x-³u)' = 3x-4 + C So u = −1+ Cx-³, and y = (−1+ Cx-³). Solving y(1) = 2 gives C = 9. 3u 3 u=y=² ⇒>> + 2xy = xy², y(0)=1. u=y-¹. 1 du 3y² dx du X - 3y³ = 3, dx 3 X So U = U=X 3 X x20 2 dy + xy + y² = 0, dx y(1) = 2. u=y-¹.

Answer rating: 100% (QA)

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