79.1.18 problem 3 (vi)

Internal problem ID [18505]
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 : 3 (vi)
Date solved : Tuesday, January 28, 2025 at 11:51:20 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 51

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

\begin{align*} x &= 3 t -\frac {\sqrt {-6 t^{3}+99 t^{2}+18 c_{1}}}{3} \\ x &= 3 t +\frac {\sqrt {-6 t^{3}+99 t^{2}+18 c_{1}}}{3} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.141 (sec). Leaf size: 67

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

\begin{align*} x(t)\to 3 t-i \sqrt {\frac {2 t^3}{3}-11 t^2-c_1} \\ x(t)\to 3 t+i \sqrt {\frac {2 t^3}{3}-11 t^2-c_1} \\ \end{align*}