MATH$-3007$: Advanced Calculus

Final Examination

Winter $2025$

$2.[6$ marks$]$ Solve the following questions for $y$ in the following differential equations. Use either the separation of variables technique or the integrating factor technique. For your final answer, be sure to algebraically isolate $y.$

$3/3$ a$.(y+3{)}^2\frac{dy}{dx}-cosx=0,$ given that $y=0$ when $x=\frac{}{2}.$

$3/3$b$.12y+3\frac{dy}{dt}-36=0,$ given that $y=0$ when $t=0$