79.1.13 problem 3 (i)

Internal problem ID [18500]
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 (i)
Date solved : Tuesday, January 28, 2025 at 11:51:07 AM
CAS classification : [_separable]

\begin{align*} 3 t^{2} x-x t +\left (3 t^{3} x^{2}+t^{3} x^{4}\right ) x^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 139

dsolve((3*t^2*x(t)-t*x(t))+(3*t^3*x(t)^2+t^3*x(t)^4)*diff(x(t),t)=0,x(t), singsol=all)
 

\begin{align*} x &= 0 \\ x &= \frac {\sqrt {-3 t^{2}+2 t \sqrt {-t \left (1+3 \ln \left (t \right ) t +c_{1} t \right )}}}{t} \\ x &= \frac {\sqrt {-3 t^{2}-2 t \sqrt {-t \left (1+3 \ln \left (t \right ) t +c_{1} t \right )}}}{t} \\ x &= -\frac {\sqrt {-3 t^{2}+2 t \sqrt {-t \left (1+3 \ln \left (t \right ) t +c_{1} t \right )}}}{t} \\ x &= -\frac {\sqrt {-3 t^{2}-2 t \sqrt {-t \left (1+3 \ln \left (t \right ) t +c_{1} t \right )}}}{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.903 (sec). Leaf size: 157

DSolve[(3*t^2*x[t]-t*x[t])+(3*t^3*x[t]^2+t^3*x[t]^4)*D[x[t],t]==0,x[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 0 \\ x(t)\to -\sqrt {-3-\frac {\sqrt {9 t-12 t \log (t)+4 c_1 t-4}}{\sqrt {t}}} \\ x(t)\to \sqrt {-3-\frac {\sqrt {9 t-12 t \log (t)+4 c_1 t-4}}{\sqrt {t}}} \\ x(t)\to -\sqrt {-3+\frac {\sqrt {9 t-12 t \log (t)+4 c_1 t-4}}{\sqrt {t}}} \\ x(t)\to \sqrt {-3+\frac {\sqrt {9 t-12 t \log (t)+4 c_1 t-4}}{\sqrt {t}}} \\ x(t)\to 0 \\ \end{align*}