79.1.22 problem 4 (iv)

Internal problem ID [18509]
Book : Elementary Differential Equations. By R.L.E. Schwarzenberger. Chapman and Hall. London. First Edition (1969)
Section : Chapter 3. Solutions of first-order equations. Exercises at page 47
Problem number : 4 (iv)
Date solved : Tuesday, January 28, 2025 at 11:51:28 AM
CAS classification : [_linear]

\begin{align*} t^{3} x^{\prime }+\left (-3 t^{2}+2\right ) x&=t^{3} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(t^3*diff(x(t),t)+(2-3*t^2)*x(t)=t^3,x(t), singsol=all)
 

\[ x = t^{3} \left (\frac {1}{2}+{\mathrm e}^{\frac {1}{t^{2}}} c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 23

DSolve[t^3*D[x[t],t]+(2-3*t^2)*x[t]==t^3,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \frac {1}{2} t^3 \left (1+2 c_1 e^{\frac {1}{t^2}}\right ) \]