75.6.6 problem 130

Internal problem ID [16762]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 130
Date solved : Tuesday, January 28, 2025 at 09:21:34 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve(x*diff(y(x),x)-2*y(x)=x^3*cos(x),y(x), singsol=all)
 

\[ y = \left (\sin \left (x \right )+c_{1} \right ) x^{2} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 22

DSolve[x*D[y[x],x]-2*y[x]==x^3*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^2 \left (\int _1^x\cos (K[1])dK[1]+c_1\right ) \]