29.26.17 problem 753
Internal
problem
ID
[5338]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
26
Problem
number
:
753
Date
solved
:
Monday, January 27, 2025 at 11:15:48 AM
CAS
classification
:
[[_homogeneous, `class G`]]
\begin{align*} {y^{\prime }}^{2}+3 x^{2}&=8 y \end{align*}
✓ Solution by Maple
Time used: 0.056 (sec). Leaf size: 153
dsolve(diff(y(x),x)^2+3*x^2 = 8*y(x),y(x), singsol=all)
\begin{align*}
y \left (x \right ) &= \frac {3 x^{2}}{8}+\frac {\operatorname {RootOf}\left (\textit {\_Z}^{6}-18 x \,\textit {\_Z}^{5}+135 x^{2} \textit {\_Z}^{4}-540 x^{3} \textit {\_Z}^{3}+\left (1215 x^{4}-16 c_{1} \right ) \textit {\_Z}^{2}+\left (-1458 x^{5}+32 c_{1} x \right ) \textit {\_Z} +729 x^{6}-16 c_{1} x^{2}\right )^{2}}{8} \\
y \left (x \right ) &= \frac {3 x^{2}}{8}+\frac {\operatorname {RootOf}\left (\textit {\_Z}^{6}+18 x \,\textit {\_Z}^{5}+135 x^{2} \textit {\_Z}^{4}+540 x^{3} \textit {\_Z}^{3}+\left (1215 x^{4}-16 c_{1} \right ) \textit {\_Z}^{2}+\left (1458 x^{5}-32 c_{1} x \right ) \textit {\_Z} +729 x^{6}-16 c_{1} x^{2}\right )^{2}}{8} \\
\end{align*}
✓ Solution by Mathematica
Time used: 21.195 (sec). Leaf size: 219
DSolve[(D[y[x],x])^2+3 x^2==8*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
\text {Solve}\left [\frac {1}{2} \text {arctanh}\left (\frac {x \sqrt {8 y(x)-3 x^2}}{3 x^2-8 y(x)}\right )-\frac {3}{2} \text {arctanh}\left (\frac {3 x \sqrt {8 y(x)-3 x^2}}{3 x^2-8 y(x)}\right )+\int \frac {3 x^3-8 x y(x)}{3 x^4-8 x^2 y(x)+4 y(x)^2} \, dx&=c_1,y(x)\right ] \\
\text {Solve}\left [-\frac {1}{2} \text {arctanh}\left (\frac {x \sqrt {8 y(x)-3 x^2}}{3 x^2-8 y(x)}\right )+\frac {3}{2} \text {arctanh}\left (\frac {3 x \sqrt {8 y(x)-3 x^2}}{3 x^2-8 y(x)}\right )+\int \frac {3 x^3-8 x y(x)}{3 x^4-8 x^2 y(x)+4 y(x)^2} \, dx&=c_1,y(x)\right ] \\
\end{align*}