Find the general solution of the differential equations:xdydx+2y=x2logx
Consider the equation a2+λx2+b2+λy2=1, where a and b are specified constants and λ is an arbitrary parameter. Find a differential equation satisfied by it.
Let f be a real-valued differentiable function on R (the set of all real numbers) such that f(1)=1. If the y−∈tercept of the tangent at any point P(x,y) on the curve y=f(x) is equal to the cube of the abscissa of P, then the value of f(−3) is equal to________
The order of the differential equation whose general solution is given by y=(C1+C2)cos(x+C3)−C4ex+C5, where C1,C2,C3,C4,C5 , are arbitrary constants, is (a) 5 (b) 4 (c) 3 (d) 2