Consider the differential equation $\frac { d y } { d x } = x ^ { 2 } + \sin x$ Solve the differential equation analytically given that $y ( 0 ) = 0$ .Then approximate $y ( 1 )$ using Euler's method with three steps.Write a few sentences describing the error in Euler's method in this case, and what could be done to decrease the error.

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The Answer of Consider the differential equation $\frac { d y } { d x } = x ^ { 2 } + \sin x$ Solve the differential equation analytically given that $y ( 0 ) = 0$ .Then approximate $y ( 1 )$ using Euler's method with three steps.Write a few sentences describing the error in Euler's method in this case, and what could be done to decrease the error.

Consider the Differential Equation dydx=x2+sin⁡x\frac { d y } { d x } = x ^ { 2 } + \sin xdxdy​=x2+sinx

Consider the Differential Equation $\frac { d y } { d x } = x ^ { 2 } + \sin x$