Solve the differential equation

Evaluate

$$g^{\prime }=m$$

Rewrite the expression

$$\frac{dg}{dm}=m$$

Transform the expression

$$dg=mdm$$

$$\text{Integrate the left-hand side of the equation with respect to }g\text{ and the right-hand side of the equation with respect to }m$$

$$\int 1dg=\int mdm$$

Calculate

More Steps

Evaluate

$$\int 1dg$$

$$\text{Use the property of integral }\int kdx=kx$$

$$g$$

$$\text{Add the constant of integral }{C}_1$$

$$g+C_1,C_1\in \mathbb{R}$$

$$g+C_1=\int mdm,C_1\in \mathbb{R}$$

Calculate

More Steps

Evaluate

$$\int mdm$$

$$\text{Use the property of integral }\int x^{n}dx=\frac{x^{n+1}}{n+1}$$

$$\frac{m^{1+1}}{1+1}$$

Add the numbers

$$\frac{m^2}{1+1}$$

Add the numbers

$$\frac{m^2}{2}$$

$$\text{Add the constant of integral }{C}_2$$

$$\frac{m^2}{2}+C_2,C_2\in \mathbb{R}$$

$$g+C_1=\frac{m^2}{2}+C_2,C_1\in \mathbb{R},C_2\in \mathbb{R}$$

Solution

$$g=\frac{m^2}{2}+C,C\in \mathbb{R}$$

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