Internal problem ID [6434]
Book: Own collection of miscellaneous problems
Section: section 2.0
Problem number: 51.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x^{3}-y x^{2}-x^{3}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-x^3*diff(y(x),x)-x^2*y(x)-x^3=0,y(x), singsol=all)
\[ y \left (x \right ) = x \operatorname {KummerM}\left (\frac {1}{2}, \frac {5}{4}, \frac {x^{4}}{4}\right ) c_{2} +x \operatorname {KummerU}\left (\frac {1}{2}, \frac {5}{4}, \frac {x^{4}}{4}\right ) c_{1} -\frac {x}{2} \]
✓ Solution by Mathematica
Time used: 0.49 (sec). Leaf size: 274
DSolve[y''[x]-x^3*y'[x]-x^2*y[x]-x^3==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \operatorname {Hypergeometric1F1}\left (\frac {1}{4},\frac {3}{4},\frac {x^4}{4}\right ) \left (\int _1^x\frac {1}{\operatorname {Hypergeometric1F1}\left (\frac {1}{4},\frac {3}{4},\frac {K[1]^4}{4}\right ) \left (\frac {3 \operatorname {Hypergeometric1F1}\left (\frac {1}{2},\frac {9}{4},\frac {K[1]^4}{4}\right )}{5 \operatorname {Hypergeometric1F1}\left (\frac {1}{2},\frac {5}{4},\frac {K[1]^4}{4}\right )}-\frac {1}{K[1]^4}\right )-\frac {2}{3} \operatorname {Hypergeometric1F1}\left (\frac {1}{4},\frac {7}{4},\frac {K[1]^4}{4}\right )}dK[1]+c_1\right )+\frac {1}{2} x \operatorname {Hypergeometric1F1}\left (\frac {1}{2},\frac {5}{4},\frac {x^4}{4}\right ) \left (\sqrt [4]{-1} \sqrt {2} \int _1^x\frac {(15-15 i) \operatorname {Hypergeometric1F1}\left (\frac {1}{4},\frac {3}{4},\frac {K[2]^4}{4}\right ) K[2]^3}{3 \operatorname {Hypergeometric1F1}\left (\frac {1}{4},\frac {3}{4},\frac {K[2]^4}{4}\right ) \left (2 \operatorname {Hypergeometric1F1}\left (\frac {3}{2},\frac {9}{4},\frac {K[2]^4}{4}\right ) K[2]^4+5 \operatorname {Hypergeometric1F1}\left (\frac {1}{2},\frac {5}{4},\frac {K[2]^4}{4}\right )\right )-5 \operatorname {Hypergeometric1F1}\left (\frac {1}{2},\frac {5}{4},\frac {K[2]^4}{4}\right ) \operatorname {Hypergeometric1F1}\left (\frac {5}{4},\frac {7}{4},\frac {K[2]^4}{4}\right ) K[2]^4}dK[2]+(1+i) c_2\right ) \\ \end{align*}