12:23 1 y+2/x y'-2/x^2 *y=lnx WolframAlpha Input 2 y'(x) + y (x) - Y(x) = log(x)...

Transcribed Image Text:

12:23 1 y"+2/x "y'-2/x^2 *y=lnx WolframAlpha Input 2 y'(x) + y (x) - Y(x) = log(x) Euler-Cauchy equation x²y" (x) + 2xy'(x) - 2 y(x) = x² log(x) ODE classification second-order linear ordinary differential equation Alternate forms 2(x y'(x) - Y(x)) 1-² +y" (x) = log(x) x²y"(x)+ 2xy'(x)-2 y(x) = log(x) = x²(Y²(x) _log(x)) + xy'(x) 2 2 y(x)= Differential equation solution 1 + x² log(x) 4 5x2 +²+c₂x 16 Step-by-step solution Plots of sample individual solutions G G x y(1) = 1 y' (1)=0 12:23 1 y"+2/x "y'-2/x^2 *y=lnx WolframAlpha Input 2 y'(x) + y (x) - Y(x) = log(x) Euler-Cauchy equation x²y" (x) + 2xy'(x) - 2 y(x) = x² log(x) ODE classification second-order linear ordinary differential equation Alternate forms 2(x y'(x) - Y(x)) 1-² +y" (x) = log(x) x²y"(x)+ 2xy'(x)-2 y(x) = log(x) = x²(Y²(x) _log(x)) + xy'(x) 2 2 y(x)= Differential equation solution 1 + x² log(x) 4 5x2 +²+c₂x 16 Step-by-step solution Plots of sample individual solutions G G x y(1) = 1 y' (1)=0

Answer rating: 100% (QA)

ANSWER To solve the given secondorder linear ordinary differential equation y 2x y 2x2 y lnx We can use the EulerCauchy equation method Step 1 Rewrite ... View the full answer