Internal problem ID [8843]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1263.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{\frac {7}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 52
dsolve(x*(x+3)*diff(diff(y(x),x),x)+(3*x-1)*diff(y(x),x)+y(x)-(20*x+30)*(x^2+3*x)^(7/3)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (c_{2}+\int \frac {\left (c_{1}+3 \left (x^{2}+3 x \right )^{\frac {7}{3}} x \left (x +3\right )\right ) \left (x +3\right )^{\frac {7}{3}}}{x^{\frac {4}{3}} \left (x^{2}+3 x \right )}d x \right ) x^{\frac {4}{3}}}{\left (x +3\right )^{\frac {7}{3}}} \]
✓ Solution by Mathematica
Time used: 10.408 (sec). Leaf size: 171
DSolve[(-30 - 20*x)*(3*x + x^2)^(7/3) + y[x] + (-1 + 3*x)*y'[x] + x*(3 + x)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-85 c_2 \left (4 \sqrt {3} x^{4/3} \text {ArcTan}\left (\frac {\sqrt {3} \sqrt [3]{x}}{\sqrt [3]{x}+2 \sqrt [3]{x+3}}\right )+4 x^{4/3} \log \left (\sqrt [3]{x+3}-\sqrt [3]{x}\right )-2 x^{4/3} \log \left (x^{2/3}+\sqrt [3]{x+3} \sqrt [3]{x}+(x+3)^{2/3}\right )+15 \sqrt [3]{x+3} x+9 \sqrt [3]{x+3}\right )+340 c_1 x^{4/3}+9 (x (x+3))^{4/3} (17 x-9) (x+3)^{13/3}}{340 (x+3)^{7/3}} \\ \end{align*}