72.7.8 problem 8

Internal problem ID [14749]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 07:13:38 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y}{1+t}+4 t^{2}+4 t \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=10 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 19

dsolve([diff(y(t),t)=y(t)/(1+t)+4*t^2+4*t,y(1) = 10],y(t), singsol=all)
 

\[ y = 2 t^{3}+2 t^{2}+3 t +3 \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 20

DSolve[{D[y[t],t]==y[t]/(1+t)+4*t^2+4*t,{y[1]==10}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 t^3+2 t^2+3 t+3 \]