Internal problem ID [13773]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.15 (e).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y=4 x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(3*x^2*diff(y(x),x$2)-7*x*diff(y(x),x)+3*y(x)=4*x^3,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{\frac {1}{3}}+\left (c_{2} +\frac {\ln \left (x \right )}{2}-\frac {3}{16}\right ) x^{3} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 33
DSolve[3*x^2*y''[x]-7*x*y'[x]+3*y[x]==4*x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} x^3 \log (x)+\left (-\frac {3}{16}+c_2\right ) x^3+c_1 \sqrt [3]{x} \]