Homogeneous Differential Equations

JEE Main Mathematics · Differential Equations · 12 questions, latest first

• Let y=y(x) be the solution of the differential equation x sin (y/x) d y=(y sin (y/x)-x) d x, y(1)=(π)/2 and let α= cos…20265 April, Shift 1 · Q25
• Let x=x(y) be the solution of the differential equation 2 y^2 (d x)/(d y)-2 x y+x^2=0, y>1, x(e)=e. Then x(e^2) is equal to:20262 April, Shift 2 · Q20
• Let the solution curve of the differential equation x d y-y d x=√(x^2+y^2) d x, x>0, y(1)=0, be y=y(x). Then y(3) is equal to202622 January, Shift 1 · Q19
• Let x=x(y) be the solution of the differential equation y=(x-y (d x)/(d y)) sin (x/y), y>0 and x(1)=(π)/2. Then cos (x(2)) is…202523 January, Shift 2 · Q19
• The solution of the differential equation (x^2+y^2) d x-5 x y d y=0, y(1)=0, is:20249 April, Shift 1 · Q10
• The solution curve of the differential equation y (d x)/(d y)=x( log_e x- log_e y+1), x>0, y>0 passing through the point (e, 1) is202431 January, Shift 1 · Q12
• If sin (y/x)= log_e|x|+(α)/2 is the solution of the differential equation x cos (y/x) (d y)/(d x)=y cos (y/x)+x and y(1)=(π)/3,…202429 January, Shift 2 · Q11
• Let f(x)=√(lim_r → x{(2 r^2[(f(r))^2-f(x) f(r)])/(r^2-x^2)-r^3 e^((f(r))/r)}) be differentiable in (-∞, 0) ∪(0, ∞) and f(1)=1.…202429 January, Shift 2 · Q28
• The slope of tangent at any point (x, y) on a curve y=y(x) is (x^2+y^2)/(2 x y), x>0. If y(2)=0, then a value of y(8) is202310 April, Shift 1 · Q10
• Let y=y(x) be the solution of the differential equation (3 y^2-5 x^2) y d x+2 x(x^2-y^2) d y=0 such that y(1)=1. Then…202331 January, Shift 2 · Q71
• The solution of the differential equation (d y)/(d x)=-((x^2+3 y^2)/(3 x^2+y^2)), y(1)=0 is202330 January, Shift 2 · Q71
• Let y=y(x) be the solution of the differential equation (x^2-3 y^2) d x+3 x y d y=0, y(1)=1. Then 6 y^2(e) is equal to202324 January, Shift 2 · Q73