Ex 9.2

Chapter 9 Class 12 Differential Equations
Serial order wise

Transcript

Ex 9.2, 8 Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : π¦βcosβ‘γπ¦=π₯γ : (π¦ sinβ‘γπ¦+cosβ‘γπ¦+π₯γ γ ) γ π¦γ^β²=π¦ π¦βcosβ‘γπ¦=π₯γ Differentiating both sides w.r.t. π₯ π/ππ₯ [π¦βγcos γβ‘π¦ ]=ππ₯/ππ₯ π(π¦)/ππ₯βπ[cos π¦]/ππ₯=1 ππ¦/ππ₯β(βsin π¦) ππ¦/ππ₯=1 ππ¦/ππ₯+π ππ π¦ ππ¦/ππ₯=1" " ππ¦/ππ₯ [1+sin π¦]=1 ππ¦/ππ₯=1/(1 + sin π¦) Now, we have to verify (π¦π ππ π¦+cos π¦+π₯) π¦^β²=π¦ Taking L.H.S (π¦ sinβ‘γπ¦+cosβ‘γπ¦+π₯γ γ ) γ π¦γ^β² =[π¦π ππ π¦+cos π¦+π¦βcosβ‘π¦ ] π¦^β² =[π¦π πππ¦+π¦] π¦^β² =π¦(1+π πππ¦) π¦^β² =π¦(1+π πππ¦)[1/(1 + sinβ‘π¦ )] =π¦ = R.H.S Hence Verified