82.40.2 problem Ex. 2

Internal problem ID [18948]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 94
Problem number : Ex. 2
Date solved : Tuesday, January 28, 2025 at 12:38:08 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{5} y^{\prime \prime }+3 x^{3} y^{\prime }+\left (3-6 x \right ) x^{2} y&=x^{4}+2 x -5 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 111

dsolve(x^5*diff(y(x),x$2)+3*x^3*diff(y(x),x)+(3-6*x)*x^2*y(x)=x^4+2*x-5,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-48 \,{\mathrm e}^{\frac {3}{x}} \operatorname {Ei}_{1}\left (\frac {3}{x}\right ) x^{5}+243 \,{\mathrm e}^{\frac {3}{x}} x^{5} c_{1} +\left (48 x^{5}+144 x^{4}+216 x^{3}+216 x^{2}+162 x \right ) \ln \left (x \right )+405+\left (1944 c_{2} +109\right ) x^{5}+\left (5832 c_{2} +471\right ) x^{4}+\left (8748 c_{2} +774\right ) x^{3}+\left (8748 c_{2} +846\right ) x^{2}+\left (6561 c_{2} +675\right ) x}{243 x^{2}} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[x^5*D[y[x],{x,2}]+3*x^2*D[y[x],x]+(3-6*x)*x^2*y[x]==x^4+2*x-5,y[x],x,IncludeSingularSolutions -> True]
 

Not solved