Exact Differential Equations

JEE Main Mathematics · Differential Equations · 3 questions, latest first

• Let y=y(x) be the solution of the differential equation x^4 d y+(4 x^3 y+2 sin x) d x=0, x>0, y((π)/2)=0. Then π^4 y((π)/3) is…202623 January, Shift 1 · Q20
• Let α|x|=|y| e^x y-β, α, β ∈ N be the solution of the differential equation x d y-y d x+x y(x d y+y d x)=0, y(1)=2. Then α+β is…20248 April, Shift 2 · Q27
• Suppose the solution of the differential equation (d y)/(d x)=((2+α) x-β y+2)/(β x-2 α y-(β γ-4 α)) represents a circle passing…20246 April, Shift 2 · Q13