Class 12

Math

Calculus

Differential Equations

Solve the following differential equation: $xdxdy =y−xtan(xy )$

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Show that the given differential equation is homogeneous and solve each of them.$yprime=xx+y $

Find the general solution of the differential equations $dxdy =4−y_{2} $ , $(−2<y<2)$

Find the general solution of the differential equation $dxdy =1+x_{2}1+y_{2} $.

Show that the differential equation $xcos(xy )dxdy =ycos(xy )+x$is homogeneous and solve it.

Find the general solution of the differential equation $dxdy =2−yx+1 ,(y=2)$

Show that the given differential equation is homogeneous and solve each of them.$(x_{2}+xy)dy=(x_{2}+y_{2})dx$

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation:$y=a_{2}−x_{2} x∈(−x,a)$ : $x+ydxdy =0(y=0)$

Find the general solution of the differential equations $dxdy =(1+x_{2})(1+y_{2})$