83.48.5 problem Ex 5 page 99

Internal problem ID [19597]
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 VII. Exact differential equations.
Problem number : Ex 5 page 99
Date solved : Tuesday, January 28, 2025 at 02:01:16 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (7 x +3\right ) y^{\prime }-3 y&=x^{2} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 28

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

\[ y \left (x \right ) = \frac {7 c_{2} x^{{5}/{2}}+x^{{7}/{2}}+7 c_{1}}{x^{{3}/{2}} \left (7 x +7\right )} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 33

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

\[ y(x)\to \frac {\frac {35 c_1}{x^{3/2}}+5 x^2+14 c_2 x}{35 x+35} \]