Question

16. (8 points) Solve the following initial value problem: \begin{equation} xy' - (2x^2 + 1)y = x^3, \quad y(1) = \frac{1}{2} \end{equation}

          16. (8 points) Solve the following initial value problem: \begin{equation*} xy' - (2x^2 + 1)y = x^3, \quad y(1) = \frac{1}{2} \end{equation*}

16. (8 points) Solve the following initial value problem:
xy' - (2x^2 + 1)y = x^3, y(1) = (1)/(2)

Added by Santiago W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/10/2023

Step 1

The integrating factor is given by: $$\mu(t) = e^{\int \frac{1}{2r^2} dt}$$ Assuming that $r$ is a constant, we have: $$\mu(t) = e^{\frac{t}{2r^2}}$$ Now, we multiply the entire differential equation by the integrating factor: $$e^{\frac{t}{2r^2}}y'(t) + Show more…

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