Question

O A Ay21 OB Ay?- (Bx+Ay) ?=5 Find the general solution of the following reducible second-order differential equation. Assume x, y andor y positive where helpful. 9yy"=5 (Bx+A) 3-5 9 9 ocy2-9(Ax+B)2=5A 2- 5 (Ax+B) 2=5 O E Ay2+9 (Ax+B)2=5 OD. Ay?-

Answer 1

Given

9y³y'' = 5

Anwer :- D. Ay² - (1/9)*(Ax + B)² = 5

In solution at end we considered all constant into two constant that is A and B.

So Please comment me for any doubt i will solve immediately.

Given qu'4"=5 0 put p=dy dx To Indepedent of Then d² did.de der da a dx. dy de day pat in equation & go ao problemas dy podralety qp² -5 2 + A y2 p² = PAY TO que

qAy²10 RAY 1.6 94² 34 P = dy QAY²-10 da 3Y 39 dy da ZAY²-10 34 -dy = x + Bi QAY²_10 pur ?Ay ²10 t ༢༩94༌། -df

3udy = 34 4A Then 3d B, dh 분 SAX + 4AR

pur BA - B 4A + 4 B 1/2 3x2* TE = 4A3 P4B, 31 put PAX +RB2 ta 2442-10. 3 174FD = 242 +2%__ Saquare both side (Pay?-18) = (29,2 +282_72 By rearranging the equation 4,4-5 = 1/A2+372 AY-1 (A2+B)2 = 5