Differential Equations

JEE Main Mathematics · 13 questions

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• Let y=y(x) be the solution of the differential equation x √(1-x^2) d y+(y √(1-x^2)-x cos^-1 x) d x=0, x ∈(0,1), lim_x → 1^-…20268 April, Shift 2 · Q17
• Let f: R → R be such that f(x y)=f(x) f(y), for all x, y ∈ R and f(0) ≠ 0. Let g:[1, ∞) → R be a differentiable function such…20266 April, Shift 2 · Q18
• Let y=y(x) be the solution of the differential equation (x^2-x √(x^2-1)) d y+(y(x-√(x^2-1))-x) d x=0, x ≥ 1. If y(1)=1, then the…20266 April, Shift 1 · Q25
• Let f:[1, ∞) → R be a differentiable function defined as f(x)=∫_1^x f(t) dt+(1-x)( log_e x-1)+e. Then the value of f(f(1)) is:20265 April, Shift 2 · Q19
• Let f(x) and g(x) be twice differentiable functions satisfying f^′ ′(x)=g^′ ′(x) for all x ∈ R, f^′(1)=2 g^′(1)=4 and g(2)=3…20265 April, Shift 2 · Q20
• Let y=y(x) be the solution of the differential equation ( tan x)^1 / 2 d y=( sec^3 x-( tan x)^3 / 2 y) d x, 0<x<(π)/2,…20265 April, Shift 2 · Q25
• 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 y=y(x) be the solution of the differential equation: (d y)/(d x)+((6 x^2+(3 x^2+2 x^3+4) e^-2 x)/((x^3+2)(2+e^-2 x)))…20264 April, Shift 2 · Q19
• Let f be a twice differentiable function such that f(x)=∫_0^x tan (t-x) d t-∫_0^x f(t) tan t d t, x ∈(-(π)/2, (π)/2). Then f^′…20264 April, Shift 2 · Q25
• Let y=y(x) be the solution of the differential equation (d y)/(d x)=(1+x+x^2)(1-y+y^2), y(0)=1/2. Then (2 y(1)-1) is equal to20264 April, Shift 1 · Q20
• 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
• If the curve y=f(x) passes through the point ( 1, e ) and satisfies the differential equation d y=y(2+ log_e x) d x, x>0, then…20262 April, Shift 1 · Q17
• Let y=y(x) be the solution curve of the differential equation (1+ sin x) (d y)/(d x)+(y+1) cos x=0, y(0)=0. If the curve y=y(x)…20262 April, Shift 1 · Q20