Internal problem ID [5441]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 34.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 150
dsolve(3*x*( y(x)^2* diff(y(x),x$3)+6*y(x)*diff(y(x),x)*diff(y(x),x$2)+2*diff(y(x),x)^3 )-3*y(x)* (y(x)*diff(y(x),x$2)+2* diff(y(x),x)^2 )=-2/x,y(x), singsol=all)
\begin{align*} y = \frac {\left (-8 c_{3} x^{3}+8 \ln \left (x \right ) x +12 c_{1} x +8 c_{2} -4 x \right )^{\frac {1}{3}}}{2} y = -\frac {\left (-8 c_{3} x^{3}+8 \ln \left (x \right ) x +12 c_{1} x +8 c_{2} -4 x \right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, \left (-8 c_{3} x^{3}+8 \ln \left (x \right ) x +12 c_{1} x +8 c_{2} -4 x \right )^{\frac {1}{3}}}{4} y = -\frac {\left (-8 c_{3} x^{3}+8 \ln \left (x \right ) x +12 c_{1} x +8 c_{2} -4 x \right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, \left (-8 c_{3} x^{3}+8 \ln \left (x \right ) x +12 c_{1} x +8 c_{2} -4 x \right )^{\frac {1}{3}}}{4} \end{align*}
✓ Solution by Mathematica
Time used: 0.297 (sec). Leaf size: 121
DSolve[3*x*( y[x]^2* y'''[x]+6*y[x]*y'[x]*y''[x]+2*y'[x]^3 )-3*y[x]* (y[x]*y''[x]+2* y'[x]^2 )==-2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt [3]{-\frac {1}{6}} \sqrt [3]{6 c_3 x^3+6 x \log (x)+(3+9 c_2) x+2 c_1} y(x)\to \sqrt [3]{c_3 x^3+x \log (x)+\frac {1}{2} (1+3 c_2) x+\frac {c_1}{3}} y(x)\to (-1)^{2/3} \sqrt [3]{c_3 x^3+x \log (x)+\frac {1}{2} (1+3 c_2) x+\frac {c_1}{3}} \end{align*}