2 points) Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One
common change of variable technique is as follows. Consider a differential equation of the form y′=f(αt+βy+γ), where α,β, and γ are constants. Use the change of variable z=αt+βy+γ to rewrite the differential equation as a separable equation of the form z′=g(z). Solve the initial value problem y′=(t+y)2−1, y(3)=4.
(a <em><u>s</u></em><em><u>q</u></em><em><u>u</u></em><em><u>a</u></em><em><u>r</u></em><em><u>e</u></em><em><u> </u></em><em><u>+</u></em><em><u>7</u></em><em><u>a</u></em><em><u>+</u></em><em><u>1</u></em><em><u>2</u></em><em><u>)</u></em><em><u> </u></em><em><u>÷</u></em><em><u>(</u></em><em><u>a</u></em><em><u>+</u></em><em><u>3</u></em><em><u>)</u></em>