29.27.30 problem 796
Internal
problem
ID
[5380]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
27
Problem
number
:
796
Date
solved
:
Monday, January 27, 2025 at 11:17:33 AM
CAS
classification
:
[[_1st_order, _with_linear_symmetries], _dAlembert]
\begin{align*} {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \end{align*}
✓ Solution by Maple
Time used: 0.051 (sec). Leaf size: 85
dsolve(diff(y(x),x)^2+3*x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*}
\frac {c_{1}}{\left (-6 x -2 \sqrt {9 x^{2}+4 y \left (x \right )}\right )^{{3}/{2}}}+\frac {2 x}{5}-\frac {\sqrt {9 x^{2}+4 y \left (x \right )}}{5} &= 0 \\
\frac {c_{1}}{\left (-6 x +2 \sqrt {9 x^{2}+4 y \left (x \right )}\right )^{{3}/{2}}}+\frac {2 x}{5}+\frac {\sqrt {9 x^{2}+4 y \left (x \right )}}{5} &= 0 \\
\end{align*}
✓ Solution by Mathematica
Time used: 13.920 (sec). Leaf size: 776
DSolve[(D[y[x],x])^2+3*x*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*}
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+40 \text {$\#$1}^4 x^2+25 \text {$\#$1}^3 x^4+160 \text {$\#$1}^2 e^{5 c_1} x+360 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-64 e^{10 c_1}\&,1\right ] \\
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+40 \text {$\#$1}^4 x^2+25 \text {$\#$1}^3 x^4+160 \text {$\#$1}^2 e^{5 c_1} x+360 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-64 e^{10 c_1}\&,2\right ] \\
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+40 \text {$\#$1}^4 x^2+25 \text {$\#$1}^3 x^4+160 \text {$\#$1}^2 e^{5 c_1} x+360 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-64 e^{10 c_1}\&,3\right ] \\
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+40 \text {$\#$1}^4 x^2+25 \text {$\#$1}^3 x^4+160 \text {$\#$1}^2 e^{5 c_1} x+360 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-64 e^{10 c_1}\&,4\right ] \\
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+40 \text {$\#$1}^4 x^2+25 \text {$\#$1}^3 x^4+160 \text {$\#$1}^2 e^{5 c_1} x+360 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-64 e^{10 c_1}\&,5\right ] \\
y(x)\to \text {Root}\left [1024 \text {$\#$1}^5+2560 \text {$\#$1}^4 x^2+1600 \text {$\#$1}^3 x^4-160 \text {$\#$1}^2 e^{5 c_1} x-360 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,1\right ] \\
y(x)\to \text {Root}\left [1024 \text {$\#$1}^5+2560 \text {$\#$1}^4 x^2+1600 \text {$\#$1}^3 x^4-160 \text {$\#$1}^2 e^{5 c_1} x-360 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,2\right ] \\
y(x)\to \text {Root}\left [1024 \text {$\#$1}^5+2560 \text {$\#$1}^4 x^2+1600 \text {$\#$1}^3 x^4-160 \text {$\#$1}^2 e^{5 c_1} x-360 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,3\right ] \\
y(x)\to \text {Root}\left [1024 \text {$\#$1}^5+2560 \text {$\#$1}^4 x^2+1600 \text {$\#$1}^3 x^4-160 \text {$\#$1}^2 e^{5 c_1} x-360 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,4\right ] \\
y(x)\to \text {Root}\left [1024 \text {$\#$1}^5+2560 \text {$\#$1}^4 x^2+1600 \text {$\#$1}^3 x^4-160 \text {$\#$1}^2 e^{5 c_1} x-360 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,5\right ] \\
y(x)\to 0 \\
\end{align*}