Differential Equations (id: c9db2a5db)

本题目来源于试卷: Differential Equations，类别为 IB数学

[填空题]
Consider the differentl*9 j ic+.7n3k2auir 2m jizzer8h6aoial equation .*twj2fexykj6y;f;r zcs6+j86atd p$\frac{\mathrm{d} y}{\mathrm{~d} x}-\frac{y}{x}=\frac{1}{2}$ , where x>0 .
1. Given that y(1)=2 , use Euler's method with step length h=0.5 to find an approximation for y(3) . Give your answer correct to two significant figures.≈   
2. Solve the equation $ \frac{\mathrm{d} y}{\mathrm{~d} x}-\frac{y}{x}=\frac{1}{2}$ for y(1)=2 .   
3. Find the percentage error when y(3) is approximated by the final rounded value found in part (a). Give your answer correct to two significant figures.≈    %

参考答案:
空格1: 7.4  空格2: 1/2*x*ln(x)+x*C  空格3: 3.2 


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