Noraml Form Differential Equations-Mathematical Physics-Assignment, Exercises of Mathematical Physics

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Question 5 If P(x)=2 for a differential equation in Normal form and one solution is given as y;= e“ cos(x). Find the other solution of the ODE. Also find the differential equation. Question 6 Find the basis of the solutions if one solution is given for the following ODE (Do not solve the equation rather find other solution from the concept of Wronskian) (a) U" (x) + 4U’ (x) +3U(x)=0 and one solution is U,= e™ (b) (x) =0 and one solution is Yi (x) =10 Question 7 If solutions of a linear homogenous ODE are given as f(x) =e , g(x) = &™ find the differential equations Question 8 If solutions of a linear homogenous ODE are given as _. _,(-4x) — _ 3x) (3X) yi= ee" ,y2=xe*” and y3=e find the differential equations. Question 9 From question No 6. Find p(x) and Wronskian. Verify the Abel’s identity P(x)W(x)=C where C is a constant. Question 10 Prove that <( P(x)W(x)) = U(x)LV(x)-V(x)LU(x) for a linear homogenous 2™ order ODE having linearly independent solutions. docsity.com