Particular Solutions to Differential Equations

Find the particular solution of the differential equation  $\frac{dy}{dx}=2x\sqrt{y}$   that satisfies the initial condition $y\left(1\right)=\frac{9}{4}$ .

•  $y=\tan^{-1}\left(x+3\right)$  

•  $y=\left(\frac{x^2}{2}+1\right)^2$  

•  $y=\tan^{-1}\left(x+2\right)$  

•  $y=-\frac{2}{x^2+3}$  

Find the particular solution of the differential equation  $\frac{dy}{dx}=\frac{2x}{e^{2y}}$  that satisfies the initial condition  $y\left(3\right)=\frac{\ln19}{2}$  .

•  $y=\ln\left(e^x+3\right)$  

•  $y=\ln\left(2e^x+1\right)$  

•  $y=\frac{\ln\left(2x^2+1\right)}{2}$  

•  $y=\frac{\ln\left(2x^{2\ }+3\right)}{2}$  

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.B.5

Find the particular solution to the differential equation  $\frac{dy}{dx}=\frac{2x^3}{y^2}$  whose graph passes through the point   $\left(2,3\right)$ .

•  $y=\ln\left(e^x+3\right)$  

•  $y=\left(\frac{3x^4}{4}+3\right)^{\frac{1}{3}}$  

•  $y=\left(\frac{3x^4}{2}+1\right)^{\frac{1}{3}}$  

•  $y=\left(\frac{3x^4}{2}+3\right)^{\frac{1}{3}}$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.1

Find the particular solution of the differential equation  $\frac{dy}{dx}=3e^{\left(x-y\right)}$  that satisfies the initial condition  $y\left(-1\right)=\ln\left(\frac{\left(e+3\right)}{e}\right)$  .

•  $y=\ln\left(3e^x+1\right)$  

•  $y=\ln\left(2e^x+3\right)$  

•  $y=\ln\left(2e^x+1\right)$  

•  $y=\ln\left(3e^x+2\right)$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSA.CED.A.1

CCSS.HSF.LE.A.4

Find the particular solution to the differential equation  $\frac{dy}{dx}=\frac{1}{\sec^2y}$  whose graph passes through the point   $\left(-3,0\right)$ .

•  $y=\sin^{-1}\left(x+1\right),\ -2<x<0$  

•  $y=\tan^{-1}\left(x+3\right)_{ }$  

•  $y=\tan^{-1}x$  

•  $y=\cos^{-1}\left(x-2\right),\ 1<x<3$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Find the particular solution to the differential equation  $\frac{dy}{dx}=3xy^2$  whose graph passes through the point   $\left(-3,-\frac{1}{14}\right)$ .

•  $y=\left(3e^x+3\right)^{\frac{1}{3}}$  

•  $y=\frac{-1}{x^2+1}$  

•  $y=\frac{-2}{3x^2+1}$  

•  $y=\frac{-2}{x^2+2}$  

Find the particular solution of the differential equation  $\frac{dy}{dx}=12x^3y$  that satisfies the initial condition  $y\left(0\right)=3$  .

•  $y=2e^{3x^4}$  

•  $y=e^{x^4}$  

•  $y=e^{2x^4}$  

•  $y=3e^{3x^4}$  

Tags

CCSS.8.EE.C.8B

Find the particular solution to the differential equation  $\frac{dy}{dx}=\frac{2xy}{x^2+1}$  whose graph passes through the point   $\left(1,\ -2\right)$ .

•  $y=3e^{2x^3}$  

•  $y=-x^2-2$  

•  $y=x^2+1$  

•  $y=-x^2-1$  

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.SSE.A.1

Find the particular solution of the differential equation  $\frac{dy}{dx}=x\sqrt{y}$  that satisfies the initial condition  $y\left(-1\right)=\frac{25}{16}$  .

•  $y=\left(\frac{x^2}{4}+1\right)^2$  

•  $y=\left(\frac{x^2}{2}+1\right)^2$  

•  $y=-e^{x^2}$  

•  $y=\left(\frac{3x^4}{4}+3\right)^{\frac{1}{3}}$  

Find the particular solution to the differential equation  $\frac{dy}{dx}=2xy+x^2y$  whose graph passes through the point   $\left(-3,-1\right)$ .

•  $y=-e^{x^2+\frac{x^3}{3}}$  

•  $y=-2e^{x^2+\frac{x^3}{3}}$  

•  $y=e^{\frac{x^2}{2}+\frac{x^3}{3}}$  

•  $y=-e^{\frac{x^2}{2}+\frac{x^3}{3}}$  

Tags

CCSS.HSA.SSE.A.1