76.2.31 problem 31

Internal problem ID [17367]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 10:03:13 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-\frac {3 y}{2}&=3 t +3 \,{\mathrm e}^{t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=y_{0} \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 25

dsolve([diff(y(t),t)-3/2*y(t)=3*t+3*exp(t),y(0) = y__0],y(t), singsol=all)
 

\[ y = -2 t -\frac {4}{3}-6 \,{\mathrm e}^{t}+{\mathrm e}^{\frac {3 t}{2}} y_{0} +\frac {22 \,{\mathrm e}^{\frac {3 t}{2}}}{3} \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 39

DSolve[{D[y[t],t]-3/2*y[t]==3*t+3*Exp[t],{y[0]==y0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{3 t/2} \left (\int _0^t3 e^{-\frac {3 K[1]}{2}} \left (K[1]+e^{K[1]}\right )dK[1]+\text {y0}\right ) \]