Internal problem ID [8008]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 532.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} \left (3+4 x \right ) y^{\prime \prime }+x \left (11+4 x \right ) y^{\prime }-\left (3+4 x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 60
dsolve(x^2*(3+4*x)*diff(y(x),x$2)+x*(11+4*x)*diff(y(x),x)-(3+4*x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \left (48 x^{2}+32 x +7\right )}{x^{3}}+\frac {c_{2} \left (48 x^{2}+32 x +7\right ) \left (\int \frac {\left (4 x +3\right )^{\frac {8}{3}} x^{\frac {7}{3}}}{\left (48 x^{2}+32 x +7\right )^{2}}d x \right )}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.313 (sec). Leaf size: 339
DSolve[x^2*(3+4*x)*y''[x]+x*(11+4*x)*y'[x]-(3+4*x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-12 \sqrt [3]{2} \sqrt {3} c_2 \left (48 x^2+32 x+7\right ) \arctan \left (\frac {\sqrt {3} \sqrt [3]{x}}{\sqrt [3]{x}+\sqrt [3]{8 x+6}}\right )+384 c_2 (4 x+3)^{2/3} x^{10/3}+576 c_2 (4 x+3)^{2/3} x^{7/3}+600 c_2 (4 x+3)^{2/3} x^{4/3}-192 \sqrt [3]{2} c_2 x \log \left (4 x^{2/3}+2 \sqrt [3]{2} \sqrt [3]{4 x+3} \sqrt [3]{x}+(8 x+6)^{2/3}\right )-42 \sqrt [3]{2} c_2 \log \left (4 x^{2/3}+2 \sqrt [3]{2} \sqrt [3]{4 x+3} \sqrt [3]{x}+(8 x+6)^{2/3}\right )+48 c_1 x^2+12 \sqrt [3]{2} c_2 \left (48 x^2+32 x+7\right ) \log \left (\sqrt [3]{8 x+6}-2 \sqrt [3]{x}\right )-288 \sqrt [3]{2} c_2 x^2 \log \left (4 x^{2/3}+2 \sqrt [3]{2} \sqrt [3]{4 x+3} \sqrt [3]{x}+(8 x+6)^{2/3}\right )+32 c_1 x+168 c_2 (4 x+3)^{2/3} \sqrt [3]{x}+7 c_1}{48 x^3} \]