List of top Mathematics Questions asked in CBSE CLASS XII

Show that the given differential equation is homogeneous and solve:\({xcos(\frac{y}{x})+ysin(\frac{y}{x})}y\,dx={ysin(\frac{y}{x})-xcos(\frac{y}{x})}x\,dy\)

Show that the given differential equation is homogeneous and solve:\(x\,dy-y\,dx=\sqrt{x^2+y^2}\,dx.\)

Show that the given differential equation is homogeneous and solve:\(x^2\frac{dy}{dx}=x^2-2y^2+xy\)

Show that the given differential equation is homogeneous and solve:\((x^2-y^2)dx+2xy\,dy=0\)

Show that the given differential equation is homogeneous and solve:\((x-y)dy-(x+y)dx=0\)

Show that the given differential equation is homogeneous and solve:\(y'=\frac{x+y}{x}\)

For the differential equations, find a particular solution satisfying the given condition:\(\frac{dy}{dx}=y tan\,\,x;y=1\) when x=0

For the differential equations, find a particular solution satisfying the given condition:\(x(x^2-1)\frac{dy}{dx}=1;y=0\) when x=2

For the differential equations , find the general solution:\(e^x tany\,\, dx+(1-e^x)sec^2y\,\,\, dy=0\)

For the differential equations , find the general solution:\(\frac{dy}{dx}=sin^{-1}x\)

For the differential equations, find the general solution:\(y\ log\ y \ dx-x\  dy=0\)

For the differential equations, find the general solution:\(\frac {dy}{dx} =(1+x^2)(1+y^2)\)

For the differential equations , find the general solution:\((e^x+e^{-x})dy-(e^x-e^{-x})dx=0\)

For the differential equations , find the general solution: \(sec^2x tan\ y \ dx+sex^2y tan\  x \ dy = 0\)

For the differential equations , find the general solution:\(\frac {dy}{dx} =\sqrt {4-y^2}, \ \ \ (-2<y<2)\)

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b:\(y=e^x(a\cos x+b\sin x)\)

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b: \(\frac{x}{a}+\frac{y}{b}=1\)

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b:y²= a(b²-x²)

Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b:\(y=ae^{3x}+be^{-2x}\)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:\(y=\sqrt{a^2-x^2}\,\,\, x∈(-a,a) :x+y  (\frac{dy}{dx})  =0(y≠0)\)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \(x+y=tan^{-1}y :y^2y'+y^2+1=0\)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \(y=x sin x : xy'=\)\(y+x\sqrt{x^2-y^2}(x\neq 0\,and x>y\,or x<-y)\)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \(y=Ax : xy'= y (x   (\neq)   0)\)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: \(y=\sqrt{1+x^2}\::y'=\frac{xy}{1+x^2}\)