60.2.239 problem 815
Internal
problem
ID
[10826]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
815
Date
solved
:
Tuesday, January 28, 2025 at 05:19:34 PM
CAS
classification
:
[[_Abel, `2nd type`, `class C`]]
\begin{align*} y^{\prime }&=\frac {\left (3+y\right )^{3} {\mathrm e}^{\frac {9 x^{2}}{2}} x \,{\mathrm e}^{\frac {3 x^{2}}{2}} {\mathrm e}^{-3 x^{2}}}{243 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 \,{\mathrm e}^{\frac {3 x^{2}}{2}} y+243 y} \end{align*}
✓ Solution by Maple
Time used: 0.007 (sec). Leaf size: 165
dsolve(diff(y(x),x) = 1/81*(3+y(x))^3*exp(9/2*x^2)*x*exp(3/2*x^2)/(3*exp(3/2*x^2)+exp(3/2*x^2)*y(x)+3*y(x))/exp(3*x^2),y(x), singsol=all)
\[
5 \ln \left (3\right )-5 \ln \left (7\right )+5 \ln \left (\frac {\left (-81 y^{2}-243 y\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+\left (3+y\right )^{2} {\mathrm e}^{3 x^{2}}-243 y^{2}}{\left ({\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y\right )+3 y\right )^{2}}\right )-\frac {30 \sqrt {93}\, \operatorname {arctanh}\left (\frac {\left (29 y \,{\mathrm e}^{\frac {3 x^{2}}{2}}+87 \,{\mathrm e}^{\frac {3 x^{2}}{2}}+81 y\right ) \sqrt {93}}{\left (279 y+837\right ) {\mathrm e}^{\frac {3 x^{2}}{2}}+837 y}\right )}{31}-10 \ln \left (\frac {{\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y\right )}{{\mathrm e}^{\frac {3 x^{2}}{2}} \left (3+y\right )+3 y}\right )+15 x^{2}-c_{1} = 0
\]
✓ Solution by Mathematica
Time used: 7.069 (sec). Leaf size: 226
DSolve[D[y[x],x] == (E^(3*x^2)*x*(3 + y[x])^3)/(81*(3*E^((3*x^2)/2) + 3*y[x] + E^((3*x^2)/2)*y[x])),y[x],x,IncludeSingularSolutions -> True]
\[
\text {Solve}\left [\int _1^{\frac {-30 e^{3 x^2} x-e^{\frac {3 x^2}{2}} \left (27+10 e^{\frac {3 x^2}{2}}\right ) y(x) x}{3\ 3^{2/3} \sqrt [3]{7} \left (3+e^{\frac {3 x^2}{2}}\right ) \sqrt [3]{-\frac {e^{\frac {9 x^2}{2}} x^3}{\left (3+e^{\frac {3 x^2}{2}}\right )^3}} \left (\left (3+e^{\frac {3 x^2}{2}}\right ) y(x)+3 e^{\frac {3 x^2}{2}}\right )}}\frac {1}{K[1]^3+\frac {10 \sqrt [3]{-\frac {1}{3}} K[1]}{7^{2/3}}+1}dK[1]+\frac {3}{2} \sqrt [3]{3} 7^{2/3} e^{-3 x^2} \left (-\frac {e^{\frac {9 x^2}{2}} x^3}{\left (e^{\frac {3 x^2}{2}}+3\right )^3}\right )^{2/3} \left (e^{\frac {3 x^2}{2}}+3\right )^2=c_1,y(x)\right ]
\]