Question

Integrate and evaluate the given equation

4. x dy dx + 3y = 3

Answer 1

a dy dre +3 - 3. => x1 dy + da + 를 3) 키 dy da + 3 3 - 3 건 조 This is the first order linear non homogeneous differential Equation in the form

dy da + -Py = 9 where P and Q are functions of a cor constants) It's solution is given by integrating factor (IF) method If = espdx and solution is give ren as Y(IF) = [9(16) dx + c y

where C is constant of integration

so for dg t dx 3 dk J IF=e 31 de If = e 3 IF=e for a70

If = e e enxe3 Pialab = ln be IFE 23 [elenb = b] and solution is given as Y(TF) = S(IF) dx + c y

3 dhe te Я 3/ 1 x 3 de xdate - х*) = 3/5 ** - 3 | х8 2 * = 3 () + - °у = х2+с 3 ос + С

3 x tc 3 с [ + с ya Sо, required solution مد - + с 8(х) = о/ ť