83.26.15 problem 15

Internal problem ID [19339]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (C) at page 93
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 01:34:34 PM
CAS classification : [[_3rd_order, _reducible, _mu_y2]]

\begin{align*} x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+7 x y^{\prime }-8 y&=x^{2}+\frac {1}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 44

dsolve(x^3*diff(y(x),x$3)-3*x^2*diff(y(x),x$2)+7*x*diff(y(x),x)-8*y(x)=x^2+1/x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {32 \ln \left (x \right )^{3} x^{4}+192 c_3 \,x^{4} \ln \left (x \right )^{2}+192 c_{2} x^{4} \ln \left (x \right )+192 c_{1} x^{4}-3}{192 x^{2}} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 48

DSolve[x^3*D[y[x],{x,3}]-3*x^2*D[y[x],{x,2}]+7*x*D[y[x],x]-8*y[x]==x^2+1/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{64 x^2}+\frac {1}{6} x^2 \log ^3(x)+c_1 x^2+c_3 x^2 \log ^2(x)+c_2 x^2 \log (x) \]