68.7.54 problem 59
Internal
problem
ID
[17418]
Book
:
INTRODUCTORY
DIFFERENTIAL
EQUATIONS.
Martha
L.
Abell,
James
P.
Braselton.
Fourth
edition
2014.
ElScAe.
2014
Section
:
Chapter
2.
First
Order
Equations.
Exercises
2.5,
page
64
Problem
number
:
59
Date
solved
:
Thursday, October 02, 2025 at 02:18:36 PM
CAS
classification
:
[_dAlembert]
\begin{align*} y&=t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3} \end{align*}
✓ Maple. Time used: 0.035 (sec). Leaf size: 734
ode:=y(t) = t*diff(y(t),t)^2+3*diff(y(t),t)^2-2*diff(y(t),t)^3;
dsolve(ode,y(t), singsol=all);
\begin{align*} \text {Solution too large to show}\end{align*}
✓ Mathematica. Time used: 141.845 (sec). Leaf size: 875
ode=y[t]==t*D[y[t],t]^2+3*D[y[t],t]^2-2*D[y[t],t]^3;
ic={};
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
\begin{align*} y(t)&\to \frac {1}{12} \left (-\frac {2 t^3}{\sqrt [3]{-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )}}-2 t \left (-6+\sqrt [3]{-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )}\right )-\left (-t^3+6 \sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+108+54 c_1\right ){}^{2/3}+t^2-\frac {t^4}{\left (-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )\right ){}^{2/3}}+36+12 c_1\right )\\ y(t)&\to \frac {1}{24} \left (\frac {2 \left (1-i \sqrt {3}\right ) t^3}{\sqrt [3]{-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )}}+2 t \left (i \sqrt {3} \sqrt [3]{-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )}+\sqrt [3]{-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )}+12\right )-i \sqrt {3} \left (-t^3+6 \sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+108+54 c_1\right ){}^{2/3}+\left (-t^3+6 \sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+108+54 c_1\right ){}^{2/3}+2 t^2+\frac {\left (1+i \sqrt {3}\right ) t^4}{\left (-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )\right ){}^{2/3}}+72+24 c_1\right )\\ y(t)&\to \frac {1}{24} \left (\frac {2 \left (1+i \sqrt {3}\right ) t^3}{\sqrt [3]{-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )}}+2 t \left (-i \sqrt {3} \sqrt [3]{-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )}+\sqrt [3]{-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )}+12\right )+i \sqrt {3} \left (-t^3+6 \sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+108+54 c_1\right ){}^{2/3}+\left (-t^3+6 \sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+108+54 c_1\right ){}^{2/3}+2 t^2+\frac {\left (1-i \sqrt {3}\right ) t^4}{\left (-t^3+6 \left (\sqrt {3} \sqrt {(2+c_1) \left (-t^3+54+27 c_1\right )}+18+9 c_1\right )\right ){}^{2/3}}+72+24 c_1\right ) \end{align*}
✗ Sympy
from sympy import *
t = symbols("t")
y = Function("y")
ode = Eq(-t*Derivative(y(t), t)**2 + y(t) + 2*Derivative(y(t), t)**3 - 3*Derivative(y(t), t)**2,0)
ics = {}
dsolve(ode,func=y(t),ics=ics)
Timed Out