83.47.7 problem Ex 7 page 87

Internal problem ID [19584]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VI. Homogeneous linear equations with variable coefficients
Problem number : Ex 7 page 87
Date solved : Tuesday, January 28, 2025 at 01:59:57 PM
CAS classification : [[_3rd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+2 y&=10 x +\frac {10}{x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 39

dsolve(x^3*diff(y(x),x$3)+2*x^2*diff(y(x),x$2)+2*y(x)=10*(x+1/x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {5 x^{2} \sin \left (\ln \left (x \right )\right ) c_3 +5 x^{2} \cos \left (\ln \left (x \right )\right ) c_{2} +25 x^{2}+10 \ln \left (x \right )+c_{1} +8}{5 x} \]

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 42

DSolve[x^3*D[y[x],{x,3}]+2*x^2*D[y[x],{x,2}]+2*y[x]==10*(x+1/x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {25 x^2+10 \log (x)+8+5 c_3}{5 x}+c_2 x \cos (\log (x))+c_1 x \sin (\log (x)) \]