Transcription of 1.10 Numerical Solution to First-Order Differential Equations
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1.10 Numerical Solution to First-Order Differential Equations
I i main . 2007/2/16. page 90. i i 90 CHAPTER 1 First-Order Differential Equations 31. Consider the general rst-order linear Differential (b) Show that the general Solution to Equation equation ( ) can be written in the form dy x . + p(x)y = q(x), ( ). dx y(x) = I 1 I (t)q(t) dt + c , where p(x) and q(x) are continuous functions on some interval (a, b). where I is given in Equation ( ), and c is an arbitrary constant. (a) Rewrite Equation ( ) in Differential form, and show that an integrating factor for the result- ing equation is.
“main” 2007/2/16 page 90 90 CHAPTER 1 First-Order Differential Equations 31. Consider the general first-order linear differential equation dy dx +p(x)y= q(x), (1.9.25) wherep(x)andq(x)arecontinuousfunctionsonsome interval (a,b). (a) Rewrite Equation (1.9.25) in differential form, and show that an integrating factor for the result-
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