Class 12

Math

Calculus

Differential Equations

Find the particular solution of the differential equation$(1−y_{2})(1+gx)dx+2xydy=0,$given that $y=0$when $x=1.$

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 double itself in 10 years $(g_{e}=0.6931)$

Find the general solution of the differential equations:$xdydx +y−x+xycotx=0(x=0)$

Show that the given differential equation is homogeneous and solve each of them.$xdy−ydx=x_{2}+y_{2} dx$

Which of the following differential equations has y = x as one of its particular solution?(A) $dx_{2}d_{2}y −x_{2}dxdy +xy=x$ (B) $dx_{2}d_{2}y +xdxdy +xy=x$ (C) $dx_{2}d_{2}y −x_{2}dxdy +xy=0$ (D) \displaystyle\frac{{{d}^{{2}}{y}}}{{{\left.{d}{x}\right.}^{{2}}}}+{x}\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}+{x}{y}={0}

Find a particular solution of the differential equation $(x+1)dxdy =2e_{−y}−1$given that $y=0$when$x=0$.

Find the general solution of the differential equations:$xdydx +2y=x_{2}gx$

In a culture, the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria is proportional to the number present?

The general solution of the differential equation $yydx−xdy =0$is(A) $xy=C$ (B) $x=Cy_{2}$ (C) $y=Cx$ (D) $y=Cx_{2}$