29.35.23 problem 1056
Internal
problem
ID
[5621]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
35
Problem
number
:
1056
Date
solved
:
Monday, January 27, 2025 at 12:29:37 PM
CAS
classification
:
[_quadrature]
\begin{align*} 4 {y^{\prime }}^{3}+4 y^{\prime }&=x \end{align*}
✓ Solution by Maple
Time used: 0.116 (sec). Leaf size: 179
dsolve(4*diff(y(x),x)^3+4*diff(y(x),x) = x,y(x), singsol=all)
\begin{align*}
y \left (x \right ) &= \frac {\left (\int \frac {\left (i \sqrt {3}-1\right ) \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{{2}/{3}}+12 i \sqrt {3}+12}{\left (27 x +3 \sqrt {81 x^{2}+192}\right )^{{1}/{3}}}d x \right )}{12}+c_{1} \\
y \left (x \right ) &= -\frac {\left (\int \frac {i \sqrt {3}\, \left (27 x +3 \sqrt {81 x^{2}+192}\right )^{{2}/{3}}+12 i \sqrt {3}+\left (27 x +3 \sqrt {81 x^{2}+192}\right )^{{2}/{3}}-12}{\left (27 x +3 \sqrt {81 x^{2}+192}\right )^{{1}/{3}}}d x \right )}{12}+c_{1} \\
y \left (x \right ) &= \frac {\left (\int \frac {\left (27 x +3 \sqrt {81 x^{2}+192}\right )^{{2}/{3}}-12}{\left (27 x +3 \sqrt {81 x^{2}+192}\right )^{{1}/{3}}}d x \right )}{6}+c_{1} \\
\end{align*}
✓ Solution by Mathematica
Time used: 2.901 (sec). Leaf size: 571
DSolve[4 (D[y[x],x])^3 +4 D[y[x],x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \frac {i \sqrt [3]{3} \left (\sqrt {3}+i\right ) \left (27 x^2-32\right ) \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}+3\ 3^{5/6} \left (1-i \sqrt {3}\right ) x \sqrt {27 x^2+64} \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}+8\ 3^{2/3} \left (1+i \sqrt {3}\right ) \left (27 x^2+16\right )-72 \sqrt [6]{3} \left (1+i \sqrt {3}\right ) x \sqrt {27 x^2+64}+48 c_1 \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}{48 \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}} \\
y(x)\to \frac {\sqrt [3]{3} \left (1+i \sqrt {3}\right ) \left (32-27 x^2\right ) \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}+3\ 3^{5/6} \left (1+i \sqrt {3}\right ) x \sqrt {27 x^2+64} \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}+8\ 3^{2/3} \left (1-i \sqrt {3}\right ) \left (27 x^2+16\right )+72 i \sqrt [6]{3} \left (\sqrt {3}+i\right ) x \sqrt {27 x^2+64}+48 c_1 \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}{48 \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}} \\
y(x)\to \frac {\left (\sqrt [3]{3} \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}-4\ 3^{2/3}\right ) \left (81 x^2-9 \left (\sqrt {81 x^2+192}-2 \sqrt [3]{3} \sqrt [3]{\sqrt {81 x^2+192}-9 x}\right ) x+8\ 3^{2/3} \left (\sqrt {81 x^2+192}-9 x\right )^{2/3}-2\ 3^{5/6} \sqrt {27 x^2+64} \sqrt [3]{\sqrt {81 x^2+192}-9 x}\right )}{72 \left (\sqrt {81 x^2+192}-9 x\right )^{4/3}}+c_1 \\
\end{align*}