General and Particular Solutions

JEE Main Mathematics · Differential Equations · 4 questions, latest first

• 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 f: R → R be a thrice differentiable odd function satisfying f^′(x) ≥ 0, f^′ ′(x)=f(x), f(0)=0, f^′(0)=3. Then 9 f( log_e 3)…20252 April, Shift 1 · Q24
• Let y=y_1(x) and y=y_2(x) be the solution curves of the differential equation (d y)/(d x)=y+7 with initial conditions y_1(0)=0…202313 April, Shift 1 · Q14
• Let f and g be twice differentiable functions on R such that f^′ ′(x)=g^′ ′(x)+6 x; f^′(1)=4 g^′(1)-3=9; f(2)=3 g(2)=12 Then…202329 January, Shift 2 · Q66