15.19.19 problem 19
Internal
problem
ID
[3303]
Book
:
Differential
Equations
by
Alfred
L.
Nelson,
Karl
W.
Folley,
Max
Coral.
3rd
ed.
DC
heath.
Boston.
1964
Section
:
Exercise
37,
page
171
Problem
number
:
19
Date
solved
:
Monday, January 27, 2025 at 07:31:52 AM
CAS
classification
:
[[_homogeneous, `class A`], _rational, _dAlembert]
\begin{align*} y {y^{\prime }}^{2}&=3 x y^{\prime }+y \end{align*}
✓ Solution by Maple
Time used: 2.039 (sec). Leaf size: 273
dsolve(diff(y(x),x)^2*y(x)=3*diff(y(x),x)*x+y(x),y(x), singsol=all)
\begin{align*}
y \left (x \right ) &= 0 \\
\ln \left (x \right )-\frac {3 \,\operatorname {arctanh}\left (\frac {3}{\sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{8}+\frac {5 \,\operatorname {arctanh}\left (\frac {9 x +8 y \left (x \right )}{5 x \sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{16}-\frac {5 \,\operatorname {arctanh}\left (\frac {-9 x +8 y \left (x \right )}{5 x \sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{16}+\frac {5 \ln \left (\frac {y \left (x \right )-2 x}{x}\right )}{16}+\frac {5 \ln \left (\frac {y \left (x \right )+2 x}{x}\right )}{16}+\frac {3 \ln \left (\frac {y \left (x \right )}{x}\right )}{8}-c_{1} &= 0 \\
\ln \left (x \right )+\frac {3 \,\operatorname {arctanh}\left (\frac {3}{\sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{8}-\frac {5 \,\operatorname {arctanh}\left (\frac {9 x +8 y \left (x \right )}{5 x \sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{16}+\frac {5 \,\operatorname {arctanh}\left (\frac {-9 x +8 y \left (x \right )}{5 x \sqrt {\frac {9 x^{2}+4 y \left (x \right )^{2}}{x^{2}}}}\right )}{16}+\frac {5 \ln \left (\frac {y \left (x \right )-2 x}{x}\right )}{16}+\frac {5 \ln \left (\frac {y \left (x \right )+2 x}{x}\right )}{16}+\frac {3 \ln \left (\frac {y \left (x \right )}{x}\right )}{8}-c_{1} &= 0 \\
\end{align*}
✓ Solution by Mathematica
Time used: 76.816 (sec). Leaf size: 2113
DSolve[D[y[x],x]^2*y[x]==3*D[y[x],x]*x+y[x],y[x],x,IncludeSingularSolutions -> True]
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