60.1.517 problem 520
Internal
problem
ID
[10531]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
520
Date
solved
:
Monday, January 27, 2025 at 08:52:07 PM
CAS
classification
:
[_quadrature]
\begin{align*} {y^{\prime }}^{3}+y^{\prime }-y&=0 \end{align*}
✓ Solution by Maple
Time used: 0.033 (sec). Leaf size: 215
dsolve(diff(y(x),x)^3+diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*}
x -6 \left (\int _{}^{y}\frac {\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{1}/{3}}}{\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{2}/{3}}-12}d \textit {\_a} \right )-c_{1} &= 0 \\
\frac {-12 \left (\int _{}^{y}\frac {\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{1}/{3}}}{-6-6 i \sqrt {3}-\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{2}/{3}}}d \textit {\_a} \right )+i \left (x -c_{1} \right ) \sqrt {3}+x -c_{1}}{1+i \sqrt {3}} &= 0 \\
\frac {12 \left (\int _{}^{y}\frac {\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{1}/{3}}}{-\left (108 \textit {\_a} +12 \sqrt {81 \textit {\_a}^{2}+12}\right )^{{2}/{3}}+\left (3 i+\sqrt {3}\right )^{2}}d \textit {\_a} \right )+i \left (x -c_{1} \right ) \sqrt {3}+c_{1} -x}{i \sqrt {3}-1} &= 0 \\
\end{align*}
✓ Solution by Mathematica
Time used: 0.483 (sec). Leaf size: 335
DSolve[-y[x] + D[y[x],x] + D[y[x],x]^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [-\frac {x}{6}+c_1\right ] \\
y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{-i 2^{2/3} \sqrt {3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}-6 i \sqrt [3]{2} \sqrt {3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [\frac {x}{12}+c_1\right ] \\
y(x)\to \text {InverseFunction}\left [\int \frac {\sqrt [3]{\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}}}{i 2^{2/3} \sqrt {3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+2^{2/3} \left (\sqrt {729 \text {$\#$1}^2+108}-27 \text {$\#$1}\right )^{2/3}+6 i \sqrt [3]{2} \sqrt {3}-6 \sqrt [3]{2}}d\text {$\#$1}\&\right ]\left [\frac {x}{12}+c_1\right ] \\
y(x)\to 0 \\
\end{align*}