Internal problem ID [10282]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 54. Change of
independent variable. Page 127
Problem number: Ex 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+y-\frac {1}{x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(x^6*diff(y(x),x$2)+3*x^5*diff(y(x),x)+y(x)=1/x^2,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\frac {1}{2 x^{2}}\right ) c_{2} +\cos \left (\frac {1}{2 x^{2}}\right ) c_{1} +\frac {1}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 32
DSolve[x^6*y''[x]+3*x^5*y'[x]+y[x]==1/x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{x^2}+c_1 \cos \left (\frac {1}{2 x^2}\right )-c_2 \sin \left (\frac {1}{2 x^2}\right ) \\ \end{align*}