29.29.18 problem 840
Internal
problem
ID
[5423]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
29
Problem
number
:
840
Date
solved
:
Monday, January 27, 2025 at 11:21:55 AM
CAS
classification
:
[[_1st_order, _with_linear_symmetries], _dAlembert]
\begin{align*} 5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \end{align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 85
dsolve(5*diff(y(x),x)^2+3*x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*}
\frac {c_{1}}{\left (-30 x -10 \sqrt {9 x^{2}+20 y \left (x \right )}\right )^{{3}/{2}}}+\frac {2 x}{5}-\frac {\sqrt {9 x^{2}+20 y \left (x \right )}}{5} &= 0 \\
\frac {c_{1}}{\left (-30 x +10 \sqrt {9 x^{2}+20 y \left (x \right )}\right )^{{3}/{2}}}+\frac {2 x}{5}+\frac {\sqrt {9 x^{2}+20 y \left (x \right )}}{5} &= 0 \\
\end{align*}
✓ Solution by Mathematica
Time used: 13.850 (sec). Leaf size: 771
DSolve[5 (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 {$\#$1}^5+8 \text {$\#$1}^4 x^2+\text {$\#$1}^3 x^4+4000 \text {$\#$1}^2 e^{5 c_1} x+1800 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-200000 e^{10 c_1}\&,1\right ] \\
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+8 \text {$\#$1}^4 x^2+\text {$\#$1}^3 x^4+4000 \text {$\#$1}^2 e^{5 c_1} x+1800 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-200000 e^{10 c_1}\&,2\right ] \\
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+8 \text {$\#$1}^4 x^2+\text {$\#$1}^3 x^4+4000 \text {$\#$1}^2 e^{5 c_1} x+1800 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-200000 e^{10 c_1}\&,3\right ] \\
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+8 \text {$\#$1}^4 x^2+\text {$\#$1}^3 x^4+4000 \text {$\#$1}^2 e^{5 c_1} x+1800 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-200000 e^{10 c_1}\&,4\right ] \\
y(x)\to \text {Root}\left [16 \text {$\#$1}^5+8 \text {$\#$1}^4 x^2+\text {$\#$1}^3 x^4+4000 \text {$\#$1}^2 e^{5 c_1} x+1800 \text {$\#$1} e^{5 c_1} x^3+216 e^{5 c_1} x^5-200000 e^{10 c_1}\&,5\right ] \\
y(x)\to \text {Root}\left [3200000 \text {$\#$1}^5+1600000 \text {$\#$1}^4 x^2+200000 \text {$\#$1}^3 x^4-4000 \text {$\#$1}^2 e^{5 c_1} x-1800 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,1\right ] \\
y(x)\to \text {Root}\left [3200000 \text {$\#$1}^5+1600000 \text {$\#$1}^4 x^2+200000 \text {$\#$1}^3 x^4-4000 \text {$\#$1}^2 e^{5 c_1} x-1800 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,2\right ] \\
y(x)\to \text {Root}\left [3200000 \text {$\#$1}^5+1600000 \text {$\#$1}^4 x^2+200000 \text {$\#$1}^3 x^4-4000 \text {$\#$1}^2 e^{5 c_1} x-1800 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,3\right ] \\
y(x)\to \text {Root}\left [3200000 \text {$\#$1}^5+1600000 \text {$\#$1}^4 x^2+200000 \text {$\#$1}^3 x^4-4000 \text {$\#$1}^2 e^{5 c_1} x-1800 \text {$\#$1} e^{5 c_1} x^3-216 e^{5 c_1} x^5-e^{10 c_1}\&,4\right ] \\
y(x)\to \text {Root}\left [3200000 \text {$\#$1}^5+1600000 \text {$\#$1}^4 x^2+200000 \text {$\#$1}^3 x^4-4000 \text {$\#$1}^2 e^{5 c_1} x-1800 \text {$\#$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*}